श्वसन (Respiration) – ऊष्माक्षेपी (Exothermic) अभिक्रिया

श्वसन (Respiration) – ऊष्माक्षेपी (Exothermic) अभिक्रिया

श्वसन (Respiration) – ऊष्माक्षेपी (Exothermic) अभिक्रिया

श्वसन (Respiration) एक ऊष्माक्षेपी (Exothermic) अभिक्रिया है। श्वसन की प्रक्रिया में जीवों द्वारा भोजन, विशेष रूप से ग्लूकोज़ (Glucose) का ऑक्सीकरण या अपघटन किया जाता है, जिससे शरीर को आवश्यक ऊर्जा प्राप्त होती है। वायवीय श्वसन में ग्लूकोज़ ऑक्सीजन की उपस्थिति में टूटकर कार्बन डाइऑक्साइड (CO₂), जल (H₂O) और ऊर्जा (ATP) का निर्माण करता है।

Class 10th Science Chapter 9 – Light – Reflection and Refraction | Image Formation by Concave Mirror

🪞 Light – Reflection and Refraction | Image Formation by Concave Mirror

Class 10 Science | CBSE + Foundation + Competitive Level

🪞 Image Formation by Concave Mirror | अवतल दर्पण द्वारा प्रतिबिम्ब निर्माण

1. Introduction | परिचय

A concave mirror is a spherical mirror whose reflecting surface is curved inward.

अवतल दर्पण वह गोलीय दर्पण है जिसकी परावर्तक सतह अन्दर की ओर मुड़ी होती है।

A concave mirror is also called a converging mirror because rays parallel to its principal axis tend to converge after reflection.

Image formation depends mainly on the position of the object with respect to P, F and C.

प्रतिबिम्ब का आकार, स्थिति और प्रकृति मुख्य रूप से वस्तु की P, F तथा C के सापेक्ष स्थिति पर निर्भर करती है।

2. Important Terms | महत्वपूर्ण पद

Term	Symbol	Meaning
Pole	P	Geometrical centre of reflecting surface
Principal Focus	F	Point where parallel rays converge after reflection
Centre of Curvature	C	Centre of the sphere of which mirror is a part
Focal Length	f	PF
Radius of Curvature	R	PC

R = 2f

3. Nature of Image | प्रतिबिम्ब की प्रकृति

The image formed by a concave mirror may be:

Real or Virtual
Inverted or Erect
Magnified, diminished or same size

The nature depends on the position of the object.

4. Important Ray Rules | महत्वपूर्ण किरण नियम

Ray Rule 1: A ray parallel to the principal axis is reflected through the principal focus F.

नियम 1: मुख्य अक्ष के समानांतर आने वाली किरण परावर्तन के बाद मुख्य फोकस F से होकर गुजरती है।

Ray Rule 2: A ray passing through F is reflected parallel to the principal axis.

नियम 2: F से होकर जाने वाली किरण परावर्तन के बाद मुख्य अक्ष के समानांतर हो जाती है।

Ray Rule 3: A ray passing through C is reflected back along the same path.

नियम 3: C से होकर जाने वाली किरण उसी मार्ग पर वापस लौटती है।

Ray Rule 4: A ray directed towards the pole obeys the laws of reflection.

5. Complete Image Formation Table ⭐

Object Position	Image Position	Size	Nature
At Infinity	At F	Highly diminished / point-sized	Real and inverted
Beyond C	Between C and F	Diminished	Real and inverted
At C	At C	Same size	Real and inverted
Between C and F	Beyond C	Magnified	Real and inverted
At F	At infinity	Highly enlarged	Real and inverted
Between F and P	Behind mirror	Magnified	Virtual and erect

6. Object at Infinity | वस्तु अनन्त पर

When the object is very far away, the incident rays reaching the concave mirror are approximately parallel to the principal axis.

After reflection, these rays converge near F.

Image: At F
Size: Highly diminished / point-sized
Nature: Real and inverted

7. Object Beyond C | C से परे वस्तु

Image forms: Between C and F
Size: Diminished
Nature: Real and inverted

8. Object at C | वस्तु C पर

When the object is placed at C, the reflected rays meet at C itself.

Image: At C
Size: Same size
Nature: Real and inverted

9. Object Between C and F | C और F के बीच वस्तु

When the object is placed between C and F, the reflected rays meet beyond C.

The image is larger than the object.

Image: Beyond C
Size: Magnified
Nature: Real and inverted

10. Object at F | वस्तु F पर

When the object is placed at the principal focus F, the reflected rays become parallel to each other. Therefore, the image is formed at infinity.

Important: The image is said to be formed at infinity. In practice, the reflected rays are parallel and do not meet at a finite point.

Image: At infinity
Size: Highly enlarged
Nature: Real and inverted

11. Object Between F and P | F और P के बीच वस्तु

When the object is placed between the principal focus F and pole P, the reflected rays diverge. Their backward extensions meet behind the mirror. Therefore, the image is virtual and erect.

Image: Behind the mirror
Size: Magnified
Nature: Virtual and erect

12. Master Ray Diagram Table ⭐

Object Position	Image Position	Relative Size	Nature
Infinity	F	Highly diminished	Real, inverted
Beyond C	Between C and F	Diminished	Real, inverted
At C	At C	Same size	Real, inverted
Between C and F	Beyond C	Magnified	Real, inverted
At F	Infinity	Highly enlarged	Real, inverted
Between F and P	Behind mirror	Magnified	Virtual, erect

13. Real and Virtual Images

Real Image: The reflected rays actually meet at the image position. It can generally be obtained on a screen.

Virtual Image: The reflected rays do not actually meet; their backward extensions appear to meet. It cannot be obtained on a screen.

Real Image	Virtual Image
Rays actually meet	Rays appear to meet
Usually inverted	Usually erect
Can be obtained on screen	Cannot be obtained on screen

14. Magnification by Concave Mirror

m = hᵢ / hₒ = -v/u

Where:
m = Magnification
hᵢ = Height of image
hₒ = Height of object
v = Image distance
u = Object distance

For a real inverted image, magnification is negative. For a virtual erect image, magnification is positive.

15. Mirror Formula

1/f = 1/v + 1/u

This equation relates focal length, object distance and image distance.

Sign convention: All distances are measured from the pole of the mirror according to the Cartesian sign convention.

16. Important Numericals

Numerical 1: A concave mirror has focal length 10 cm. Find its radius of curvature.

R = 2f
R = 2 × 10
R = 20 cm

Numerical 2: A concave mirror has radius of curvature 40 cm. Find its focal length.

f = R/2
f = 40/2
f = 20 cm

Numerical 3: An object is placed 30 cm in front of a concave mirror of focal length 15 cm. Find the image distance using the Cartesian sign convention.

Given:
u = -30 cm
f = -15 cm

Using:
1/f = 1/v + 1/u

1/(-15) = 1/v + 1/(-30)

1/v = -1/15 + 1/30
1/v = -1/30
v = -30 cm

The image is formed 30 cm in front of the mirror, at C.

Numerical 4: For the above case, find magnification.

m = -v/u
m = -(-30)/(-30)
m = -1

Negative sign indicates an inverted image. Magnitude 1 indicates same size.

17. 30 MCQs | Multiple Choice Questions

Q1. A concave mirror is also called a:

A. Converging mirror

B. Diverging mirror

C. Plane mirror

D. Transparent mirror

Answer: A

Q2. When an object is at infinity, its image by a concave mirror is formed at:

A. C

B. F

C. P

D. Behind the mirror

Answer: B

Q3. An object beyond C forms an image:

A. Beyond C

B. At C

C. Between C and F

D. Behind mirror

Answer: C

Q4. When the object is at C, the image is formed:

A. At F

B. Beyond C

C. Behind mirror

D. At C

Answer: D

Q5. The image formed when object is at C is:

A. Same size and inverted

B. Enlarged and erect

C. Diminished and erect

D. Virtual and enlarged

Answer: A

Q6. If the object lies between C and F, the image is formed:

A. At F

B. Beyond C

C. Between F and P

D. Behind mirror

Answer: B

Q7. The image formed for an object between C and F is:

A. Diminished

B. Same size

C. Magnified

D. Point-sized

Answer: C

Q8. If an object is placed at F, the reflected rays are:

A. Converging at C

B. Converging at P

C. Diverging towards C

D. Parallel

Answer: D

Q9. When object is at F, the image is formed:

A. At infinity

B. At C

C. At P

D. Behind mirror

Answer: A

Q10. An object between F and P produces an image:

A. At C

B. Behind the mirror

C. Between C and F

D. At infinity

Answer: B

Q11. The image formed by a concave mirror for an object between F and P is:

A. Real and inverted

B. Real and same size

C. Virtual and erect

D. Real and diminished

Answer: C

Q12. For an object between F and P, the image is:

A. Diminished

B. Same size

C. Point-sized

D. Magnified

Answer: D

Q13. A real image is formed when:

A. Reflected rays actually meet

B. Rays only appear to meet

C. Rays pass through P

D. Mirror is transparent

Answer: A

Q14. A virtual image cannot generally be:

A. Erect

B. Obtained on a screen

C. Magnified

D. Seen by the eye

Answer: B

Q15. The magnification formula for a spherical mirror is:

A. m = u/v

B. m = v/u

C. m = -v/u

D. m = uv

Answer: C

Q16. The mirror formula is:

A. 1/f = 1/u − 1/v

B. f = u + v

C. 1/f = u + v

D. 1/f = 1/v + 1/u

Answer: D

Q17. If m = -1, the image is:

A. Same size and inverted

B. Magnified and erect

C. Diminished and erect

D. Virtual and same size

Answer: A

Q18. If magnification is positive for a concave mirror, the image is:

A. Inverted

B. Erect

C. Always diminished

D. At infinity

Answer: B

Q19. A ray parallel to the principal axis after reflection passes through:

A. P

B. C

C. F

D. Infinity

Answer: C

Q20. A ray passing through F after reflection becomes:

A. Perpendicular to mirror

B. Towards C

C. Divergent

D. Parallel to principal axis

Answer: D

Q21. A ray passing through C is reflected:

A. Along the same path

B. Through F only

C. Parallel to axis

D. Behind mirror

Answer: A

Q22. If f = 12 cm, R is:

A. 6 cm

B. 24 cm

C. 12 cm

D. 36 cm

Answer: B

Q23. If R = 50 cm, f is:

A. 50 cm

B. 100 cm

C. 25 cm

D. 10 cm

Answer: C

Q24. A concave mirror forms a magnified virtual image when the object is:

A. Beyond C

B. At C

C. Between C and F

D. Between F and P

Answer: D

Q25. A concave mirror forms a same-size image when the object is:

A. At C

B. Beyond C

C. At F

D. Between F and P

Answer: A

Q26. A diminished real image is formed when the object is:

A. Between F and P

B. Beyond C

C. At F

D. At C

Answer: B

Q27. At the focus, the image is considered to be:

A. Diminished

B. Same size

C. Highly enlarged at infinity

D. Virtual and diminished

Answer: C

Q28. Which image can be obtained on a screen?

A. Virtual image only

B. Both always

C. Neither

D. Real image

Answer: D

Q29. For a real image formed by a concave mirror, magnification is generally:

A. Negative

B. Positive

C. Zero always

D. Infinite always

Answer: A

Q30. The position of the image changes as the object moves:

A. Only at infinity

B. Relative to P, F and C

C. Only at P

D. Only behind the mirror

Answer: B

18. 30 Subjective Questions with Answers

2 Marks Q1. What type of mirror is a concave mirror?

A concave mirror is a spherical mirror with an inward-curved reflecting surface. It is a converging mirror.

2 Marks Q2. What happens when an object is placed at infinity?

The image is formed at F. It is highly diminished, real and inverted.

2 Marks Q3. Where is the image formed when the object is at C?

The image is formed at C itself.

2 Marks Q4. What is the nature of image when object is at C?

It is real, inverted and of the same size as the object.

2 Marks Q5. What happens when the object is placed between F and P?

A virtual, erect and magnified image is formed behind the mirror.

3 Marks Q6. What happens when an object is placed beyond C?

The image is formed between C and F. It is real, inverted and diminished.

3 Marks Q7. What happens when an object is placed between C and F?

The image is formed beyond C. It is real, inverted and magnified.

3 Marks Q8. What happens when an object is placed at F?

The reflected rays become parallel and the image is formed at infinity. It is highly enlarged and inverted.

3 Marks Q9. State the mirror formula.

1/f = 1/v + 1/u

3 Marks Q10. Write the magnification formula for a mirror.

m = hᵢ/hₒ = -v/u

4 Marks Q11. Explain image formation when the object is beyond C.

When the object is beyond C, one ray parallel to the principal axis is reflected through F and another ray through C retraces its path. The rays meet between C and F. The image is real, inverted and diminished.

4 Marks Q12. Explain image formation when the object is at C.

The reflected rays meet at C. The image is formed at C and is real, inverted and equal in size to the object.

4 Marks Q13. Explain image formation when the object lies between C and F.

The reflected rays meet beyond C. The image is real, inverted and magnified.

4 Marks Q14. Explain image formation when the object lies between F and P.

The reflected rays diverge. Their backward extensions meet behind the mirror. Hence the image is virtual, erect and magnified.

4 Marks Q15. Why is the image formed at infinity when the object is at F?

A ray through F becomes parallel to the principal axis after reflection. Therefore, the reflected rays are parallel and do not meet at a finite distance. The image is considered to be at infinity.

5 Marks Q16. Write the complete table of image formation by a concave mirror.

Object	Image	Nature
Infinity	F	Real, inverted, highly diminished
Beyond C	Between C and F	Real, inverted, diminished
C	C	Real, inverted, same size
Between C and F	Beyond C	Real, inverted, magnified
F	Infinity	Real, inverted, highly enlarged
Between F and P	Behind mirror	Virtual, erect, magnified

5 Marks Q17. Explain the four important ray rules used for concave mirrors.

1. Parallel ray → reflected through F.
2. Ray through F → reflected parallel to principal axis.
3. Ray through C → retraces its path.
4. Ray directed towards P → obeys the laws of reflection.

5 Marks Q18. Differentiate between real and virtual images.

A real image is formed by actual intersection of rays and can be obtained on a screen. A virtual image is formed by apparent intersection of backward extensions of rays and cannot be obtained on a screen.

5 Marks Q19. What is magnification? Write its formula and explain its sign.

Magnification is the ratio of image height to object height.

m = hᵢ/hₒ = -v/u

Negative magnification indicates an inverted image, while positive magnification indicates an erect image.

5 Marks Q20. Why does a concave mirror produce both real and virtual images?

When the object is outside F, reflected rays can actually converge and form a real image. When the object lies between F and P, reflected rays diverge and their backward extensions meet behind the mirror, producing a virtual image.

6 Marks Q21. An object is placed beyond C. Explain the image formation using ray construction.

Draw one ray parallel to the principal axis; after reflection it passes through F. Draw another ray through C; it returns along the same path. The reflected rays intersect between C and F. Thus, the image is real, inverted and diminished.

6 Marks Q22. An object is placed between C and F. Describe the image.

The reflected rays converge beyond C. The image is therefore formed beyond C. It is real, inverted and magnified.

6 Marks Q23. An object is placed at C. What will be the position, size and nature of image?

Position: C
Size: Same as object
Nature: Real and inverted
Magnification: -1

6 Marks Q24. A concave mirror has f = 20 cm. Find R.

R = 2f
R = 2 × 20
R = 40 cm

6 Marks Q25. A concave mirror has R = 80 cm. Find f.

f = R/2
f = 80/2
f = 40 cm

6 Marks Q26. An object is placed at F. Why can its image not be obtained on an ordinary screen at a finite distance?

At F, the reflected rays become parallel. Since parallel rays do not meet at a finite point, no finite image position exists. The image is considered to be at infinity.

6 Marks Q27. Why is the image virtual when the object is between F and P?

In this position, reflected rays diverge and do not actually meet. Their backward extensions appear to meet behind the mirror. Hence the image is virtual.

6 Marks Q28. Explain the significance of the negative sign in magnification.

A negative value of magnification means that the image is inverted with respect to the object. For example, m = -1 indicates an inverted image of the same size.

6 Marks Q29. A concave mirror forms a magnified erect image. Where must the object be placed?

The object must be placed between the pole P and principal focus F.

6 Marks Q30. A concave mirror forms a diminished real image. Give the object position.

The object must be placed beyond C. The image is then formed between C and F and is diminished, real and inverted.

19. Assertion–Reason Questions

Q1. Assertion: An object placed at C forms an image at C.
Reason: A ray passing through C retraces its path after reflection.

Answer: Both Assertion and Reason are true, and the Reason correctly supports the ray construction.

Q2. Assertion: An object between F and P produces a virtual image.
Reason: The reflected rays diverge and their backward extensions meet behind the mirror.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

Q3. Assertion: An object at F forms its image at infinity.
Reason: Reflected rays become parallel.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

Q4. Assertion: The image formed by a concave mirror for an object beyond C is diminished.
Reason: The image is formed between C and F.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

Q5. Assertion: A virtual image formed by a concave mirror is erect.
Reason: The reflected rays actually meet behind the mirror.

Answer: Assertion is true, but Reason is false. The rays do not actually meet behind the mirror; their backward extensions appear to meet.

20. HOTS | Higher Order Thinking Questions

HOTS 1: A concave mirror is required to produce a magnified virtual image. Where should the object be placed?

Between F and P.

HOTS 2: A student obtains a real, inverted and diminished image. Give the possible object position.

The object is beyond C.

HOTS 3: If the object is moved from beyond C towards F, how does the image size change?

The image becomes progressively larger. At C it is same size, and between C and F it becomes magnified.

HOTS 4: Why is a concave mirror suitable for producing a magnified image when an object is close to the mirror?

When the object is placed between F and P, the reflected rays diverge and their backward extensions form a virtual, erect and magnified image behind the mirror.

HOTS 5: An object is placed at C and then moved slightly towards F. What happens to the image?

The image moves beyond C and becomes magnified while remaining real and inverted.

21. Diagram Labelling Practice

Labels to practise:

P → Pole
F → Principal Focus
C → Centre of Curvature
PF → Focal Length
PC → Radius of Curvature
P–C line → Principal Axis

22. CBSE Golden Points ⭐

• Concave mirror is a converging mirror.
• Object at infinity → image at F.
• Object beyond C → image between C and F.
• Object at C → image at C.
• Object between C and F → image beyond C.
• Object at F → image at infinity.
• Object between F and P → virtual, erect and magnified image behind mirror.
• All real images formed by a concave mirror are inverted.
• For a virtual image by a concave mirror, the image is erect.
• Real images can be obtained on a screen.
• Virtual images cannot be obtained on a screen.
• Mirror formula: 1/f = 1/v + 1/u.
• Magnification: m = -v/u.
• R = 2f.
• Negative magnification indicates an inverted image.
• Positive magnification indicates an erect image.

23. Memory Trick 🧠

Infinity → F
Beyond C → C-F
C → C
C-F → Beyond C
F → Infinity
F-P → Behind Mirror

∞ → F → C-F → C → Beyond C → ∞

Easy Trick:

Object moves from infinity towards mirror:
Image moves from F → C → Beyond C → Infinity → Behind mirror.

24. One-Line Revision

Beyond C → Between C-F → Diminished → Real + Inverted

At C → At C → Same Size → Real + Inverted

C-F → Beyond C → Magnified → Real + Inverted

At F → Infinity → Highly Enlarged → Real + Inverted

F-P → Behind Mirror → Magnified → Virtual + Erect

25. Final Summary | अंतिम सारांश

The image formation by a concave mirror depends on the position of the object relative to the pole P, focus F and centre of curvature C.

Most important cases:

Object at infinity → Image at F.
Object beyond C → Image between C and F.
Object at C → Image at C.
Object between C and F → Image beyond C.
Object at F → Image at infinity.
Object between F and P → Virtual, erect and magnified image behind the mirror.

Important formulas:

R = 2f

1/f = 1/v + 1/u

m = hᵢ/hₒ = -v/u

🪞 Image Formation by Concave Mirror

Class 10 Science | Light – Reflection and Refraction

∞ → F → C-F → C → Beyond C → ∞ → Behind Mirror

Class 10th Science Chapter 9 – Light – Reflection and Refraction | Terms Related to Spherical Mirrors

🪞 Light – Reflection and Refraction | Terms Related to Spherical Mirrors

Class 10 Science | CBSE + Foundation + Competitive Level

🪞 Terms Related to Spherical Mirrors | गोलीय दर्पण से संबंधित पद

1. Introduction | परिचय

A spherical mirror is a reflecting surface that forms a part of a hollow sphere.

गोलीय दर्पण वह परावर्तक सतह है जो किसी खोखले गोले के एक भाग के रूप में बनी होती है।

There are two main types of spherical mirrors:

Concave Mirror | अवतल दर्पण Convex Mirror | उत्तल दर्पण

Concave Mirror: The reflecting surface is curved inward.
Convex Mirror: The reflecting surface is curved outward.

2. Basic Terms of a Spherical Mirror

3. Pole (P) | ध्रुव

The pole is the geometric centre of the reflecting surface of a spherical mirror.

It is represented by P.

Hindi: गोलीय दर्पण की परावर्तक सतह के ज्यामितीय केन्द्र को ध्रुव कहते हैं।

Remember:
P = Pole
Pole is the reference point from which distances are measured in the mirror sign convention.

4. Aperture | द्वारक

The aperture of a spherical mirror refers to the effective diameter or width of its reflecting surface.

सरल शब्दों में, दर्पण की परावर्तक सतह की प्रभावी चौड़ाई/व्यास को उसका द्वारक (Aperture) कहा जाता है।

Aperture = Effective diameter of reflecting surface

For school-level ray diagrams, the aperture is usually represented by the width of the mirror's reflecting surface.

5. Centre of Curvature (C) | वक्रता केन्द्र

The centre of curvature is the centre of the sphere of which the spherical mirror forms a part.

It is represented by C.

गोलीय दर्पण जिस खोखले गोले का भाग होता है, उस गोले के केन्द्र को वक्रता केन्द्र (C) कहते हैं।

Important:
For a concave mirror, C lies in front of the mirror.
For a convex mirror, C lies behind the mirror.

6. Radius of Curvature (R) | वक्रता त्रिज्या

The distance between the pole P and the centre of curvature C is called the radius of curvature.

R = PC

Here:
R = Radius of curvature
P = Pole
C = Centre of curvature

7. Principal Axis | मुख्य अक्ष

The straight line passing through the pole P and centre of curvature C of a spherical mirror is called the principal axis.

गोलीय दर्पण के ध्रुव P और वक्रता केन्द्र C से होकर गुजरने वाली सीधी रेखा को मुख्य अक्ष कहते हैं।

Principal Axis → P and C lie on it

8. Principal Focus (F) | मुख्य फोकस

The point on the principal axis where rays parallel to the principal axis converge after reflection from a concave mirror is called its principal focus.

For a convex mirror, parallel rays appear to diverge from a point behind the mirror. This point is called its principal focus.

Mirror	Principal Focus
Concave Mirror	Real focus in front of mirror
Convex Mirror	Virtual focus behind mirror

9. Focal Length (f) | फोकस दूरी

The distance between the pole P and principal focus F is called the focal length.

f = PF

The focal length is generally taken as half of the radius of curvature for a spherical mirror under the usual paraxial approximation.

R = 2f

f = R/2

10. Relation Between P, F and C

Important relation:

PF = FC
PC = 2PF
Therefore:
R = 2f

11. Position of P, F and C in Concave Mirror

For a concave mirror:

Mirror ← F ← C

Both F and C lie in front of the reflecting surface.

12. Position of P, F and C in Convex Mirror

For a convex mirror, F and C are located behind the reflecting surface.

Therefore, F and C are virtual points for a convex mirror.

13. Normal to a Spherical Mirror

The normal at any point on a spherical mirror passes through the centre of curvature C.

Thus, a radius drawn from C to a point on the spherical reflecting surface is normal to the surface at that point.

Normal → Line joining point of incidence to C

This concept is particularly useful when studying the law of reflection on spherical mirrors.

14. All Important Terms at a Glance

Term	Symbol	Meaning
Pole	P	Geometrical centre of reflecting surface
Centre of Curvature	C	Centre of the sphere of which mirror is a part
Radius of Curvature	R	Distance PC
Principal Axis	—	Line passing through P and C
Principal Focus	F	Point related to convergence/apparent divergence of parallel rays
Focal Length	f	Distance PF
Aperture	—	Effective diameter/width of reflecting surface

15. Concave and Convex Mirror – Terms Comparison

Property	Concave	Convex
Reflecting surface	Inward curved	Outward curved
C position	In front	Behind
F position	In front	Behind
Nature	Converging	Diverging
Focus	Real	Virtual

16. Parallel Ray and Principal Focus

Rule: A ray parallel to the principal axis, after reflection from a concave mirror, passes through F.

For a convex mirror, it appears to diverge from F behind the mirror.

17. Basic Numerical Concepts

R = 2f

If f = 15 cm:

R = 2 × 15 = 30 cm

f = R/2

If R = 60 cm:

f = 60/2 = 30 cm

18. 30 MCQs | Multiple Choice Questions

Q1. A spherical mirror is a part of a:

A. Hollow sphere

B. Cube

C. Cylinder only

D. Plane

Answer: A

Q2. The geometrical centre of the reflecting surface is called:

A. Focus

B. Pole

C. Centre of curvature

D. Aperture

Answer: B

Q3. The symbol used for pole is:

A. C

B. F

C. P

D. R

Answer: C

Q4. The centre of the sphere of which the mirror is a part is called:

A. Pole

B. Focus

C. Aperture

D. Centre of curvature

Answer: D

Q5. Centre of curvature is represented by:

A. C

B. P

C. F

D. R

Answer: A

Q6. The distance PC is called:

A. Focal length

B. Radius of curvature

C. Aperture

D. Object distance

Answer: B

Q7. The distance PF is called:

A. Radius of curvature

B. Diameter

C. Focal length

D. Aperture

Answer: C

Q8. The principal axis passes through:

A. F only

B. C only

C. P only

D. P and C

Answer: D

Q9. The relation between R and f is:

A. R = 2f

B. R = f/2

C. R = f

D. R = 4f

Answer: A

Q10. If f = 10 cm, R is:

A. 5 cm

B. 20 cm

C. 10 cm

D. 40 cm

Answer: B

Q11. In a concave mirror, C lies:

A. Behind mirror

B. At P

C. In front of mirror

D. At infinity only

Answer: C

Q12. In a convex mirror, C lies:

A. In front

B. At P

C. On mirror surface

D. Behind the mirror

Answer: D

Q13. The principal focus of a concave mirror is:

A. In front of mirror

B. Behind mirror

C. At infinity

D. At P always

Answer: A

Q14. The principal focus of a convex mirror is:

A. In front

B. Behind the mirror

C. At C in front

D. At P

Answer: B

Q15. The focal length is represented by:

A. R

B. C

C. f

D. P

Answer: C

Q16. The distance PF represents:

A. Radius

B. Aperture

C. Diameter

D. Focal length

Answer: D

Q17. Aperture of a spherical mirror refers to its:

A. Effective diameter/width of reflecting surface

B. Focal length

C. Radius only

D. Image distance

Answer: A

Q18. A line passing through P and C is called:

A. Focal line

B. Principal axis

C. Normal only

D. Aperture line

Answer: B

Q19. A ray parallel to the principal axis of a concave mirror is reflected through:

A. P

B. C

C. F

D. Infinity

Answer: C

Q20. For a convex mirror, parallel rays appear to come from:

A. C in front

B. P

C. Infinity

D. F behind mirror

Answer: D

Q21. If R = 50 cm, f is:

A. 25 cm

B. 50 cm

C. 100 cm

D. 10 cm

Answer: A

Q22. If focal length is 30 cm, radius of curvature is:

A. 15 cm

B. 60 cm

C. 30 cm

D. 90 cm

Answer: B

Q23. The point F is located halfway between:

A. P and C

B. P and mirror edge

C. C and infinity

D. P and aperture

Answer: A

Q24. The normal at a point on a spherical mirror passes through:

A. P only

B. C

C. F only

D. Aperture

Answer: B

Q25. Which mirror has its focus behind the mirror?

A. Concave

B. Plane

C. Convex

D. None

Answer: C

Q26. Which point is the reference from which mirror distances are measured?

A. C

B. F

C. Centre of aperture

D. P

Answer: D

Q27. If PC = 80 cm, PF is:

A. 40 cm

B. 80 cm

C. 160 cm

D. 20 cm

Answer: A

Q28. Which one is not a basic term of spherical mirrors?

A. Pole

B. Focal length

C. Centre of curvature

D. Electric current

Answer: D

Q29. For a spherical mirror, the usual paraxial relation is:

A. R = 2f

B. R = f/2

C. R = f

D. R = 3f

Answer: A

Q30. Which sequence correctly represents the points for a concave mirror?

A. P–C–F

B. C–F–P

C. F–P–C

D. C–P–F

Answer: B

19. 30 Subjective Questions with Answers

2 Marks Q1. What is a spherical mirror?

A spherical mirror is a reflecting surface that forms a part of a hollow sphere.

2 Marks Q2. Define the pole of a spherical mirror.

The pole is the geometrical centre of the reflecting surface of a spherical mirror.

2 Marks Q3. What is centre of curvature?

It is the centre of the sphere of which the spherical mirror is a part.

2 Marks Q4. Define radius of curvature.

The distance between P and C is called the radius of curvature.
R = PC

2 Marks Q5. What is focal length?

The distance between the pole P and principal focus F is called focal length.
f = PF

3 Marks Q6. Define principal axis.

The straight line passing through the pole P and centre of curvature C is called the principal axis.

3 Marks Q7. What is principal focus of a concave mirror?

It is the point on the principal axis where rays parallel to the principal axis converge after reflection.

3 Marks Q8. What is principal focus of a convex mirror?

It is the point behind the mirror from which parallel reflected rays appear to diverge.

3 Marks Q9. Write the relation between radius of curvature and focal length.

R = 2f

3 Marks Q10. What is aperture of a spherical mirror?

Aperture refers to the effective diameter or width of the reflecting surface of the spherical mirror.

4 Marks Q11. Differentiate between pole and centre of curvature.

Pole	Centre of Curvature
Geometrical centre of reflecting surface	Centre of the sphere of which mirror is a part
Represented by P	Represented by C

4 Marks Q12. Differentiate between focal length and radius of curvature.

Focal length is PF, whereas radius of curvature is PC.

f = PF
R = PC
For a spherical mirror under the usual paraxial approximation: R = 2f

4 Marks Q13. Explain the position of P, F and C in a concave mirror.

For a concave mirror, P is on the reflecting surface, while F and C lie in front of the mirror. F lies approximately halfway between P and C.

4 Marks Q14. Explain the position of P, F and C in a convex mirror.

P lies on the reflecting surface. F and C lie behind the mirror. F lies between P and C.

4 Marks Q15. What is meant by principal axis?

The line passing through P and C is called the principal axis. It is the main reference line used in spherical-mirror ray diagrams.

5 Marks Q16. Explain all important terms related to a spherical mirror.

The important terms are pole, centre of curvature, radius of curvature, principal axis, principal focus, focal length and aperture. P is the centre of the reflecting surface, C is the centre of the parent sphere, R = PC, F is the principal focus, f = PF, and aperture represents the effective diameter/width of the reflecting surface.

5 Marks Q17. Explain the relation R = 2f.

For a spherical mirror under the usual paraxial approximation, the principal focus F lies approximately midway between P and C. Hence PF = FC. Therefore PC = PF + FC = 2PF. Thus, R = 2f.

5 Marks Q18. Explain the principal focus of concave and convex mirrors.

In a concave mirror, parallel rays converge at F in front of the mirror, so the focus is real. In a convex mirror, parallel rays diverge after reflection and their backward extensions meet at F behind the mirror, so the focus is virtual.

5 Marks Q19. Why is the centre of curvature important in spherical mirrors?

It defines the geometry of the spherical mirror and helps locate the principal axis, radius of curvature and focus. A ray directed through C strikes the spherical surface normally and retraces its path.

5 Marks Q20. Explain the importance of aperture.

Aperture represents the effective diameter or width of the reflecting surface. It indicates the portion of the mirror available for receiving and reflecting light.

6 Marks Q21. Draw and explain the basic terms of a concave spherical mirror.

The diagram should show P, F, C and the principal axis. P is the pole, F is the principal focus, C is the centre of curvature, PF is focal length and PC is radius of curvature. F lies approximately halfway between P and C.

6 Marks Q22. Explain the basic terms of a convex spherical mirror.

For a convex mirror, P is on the reflecting surface while F and C lie behind the mirror. F is between P and C. PF represents focal length and PC represents radius of curvature. The mirror acts as a diverging mirror.

6 Marks Q23. A spherical mirror has focal length 20 cm. Find its radius of curvature.

Given:
f = 20 cm

Using:
R = 2f

R = 2 × 20

R = 40 cm

6 Marks Q24. A spherical mirror has radius of curvature 80 cm. Find its focal length.

Given:
R = 80 cm

f = R/2

f = 80/2

f = 40 cm

6 Marks Q25. If PF = 15 cm, find PC.

PF = f = 15 cm

PC = R = 2f

R = 2 × 15

PC = 30 cm

6 Marks Q26. If PC = 100 cm, find PF.

PC = R = 100 cm

PF = f = R/2

f = 100/2

PF = 50 cm

6 Marks Q27. Why does a ray passing through C retrace its path?

At any point on a spherical mirror, the radius drawn from C to that point is normal to the surface. Therefore, a ray directed through C strikes the mirror normally. Its angle of incidence is zero, so it is reflected back along the same path.

6 Marks Q28. Compare the positions of F and C in concave and convex mirrors.

Concave	Convex
F in front of mirror	F behind mirror
C in front of mirror	C behind mirror
F lies between P and C	F lies between P and C behind the mirror

6 Marks Q29. Explain the difference between real focus and virtual focus in spherical mirrors.

A real focus is a point where reflected rays actually meet. The focus of a concave mirror is real. A virtual focus is a point from which reflected rays appear to diverge when extended backward. The focus of a convex mirror is virtual.

6 Marks Q30. A student says that F and C are the same point in a spherical mirror. Is the statement correct?

No. F and C are different points. F lies approximately halfway between P and C. Therefore, R = PC = 2PF = 2f.

20. Assertion–Reason Questions

Q1. Assertion: The distance PC is called radius of curvature.
Reason: C is the centre of the sphere of which the mirror is a part.

Answer: Both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Q2. Assertion: The principal axis passes through P and C.
Reason: P and C are important geometrical reference points of a spherical mirror.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

Q3. Assertion: The focus of a convex mirror is virtual.
Reason: Reflected parallel rays actually meet behind the mirror.

Answer: Assertion is true, but Reason is false. The reflected rays do not actually meet; their backward extensions appear to meet.

Q4. Assertion: R = 2f for a spherical mirror under the usual paraxial approximation.
Reason: F lies approximately midway between P and C.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

Q5. Assertion: The normal to a spherical mirror at a point passes through C.
Reason: The radius drawn from the centre of the sphere to the surface is normal to the spherical surface.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

21. HOTS | Higher Order Thinking

HOTS 1: A mirror has R = 60 cm. Without using the mirror formula, determine its focal length.

f = R/2 = 60/2 = 30 cm.

HOTS 2: Why is C behind the mirror for a convex mirror?

A convex mirror is part of a sphere whose centre lies on the opposite side of the reflecting surface. Therefore, C is located behind the mirror.

HOTS 3: If a ray is directed towards C of a spherical mirror, why does it return along the same path?

Because the radius from C to the point of incidence is normal to the spherical surface. Hence i = 0° and the ray retraces its path.

HOTS 4: If the focal length of a spherical mirror is increased, what happens to its radius of curvature?

Since R = 2f, the radius of curvature also increases in the same proportion.

HOTS 5: A student marks F halfway between P and C. Is this always an exact geometrical rule?

At Class 10 level, F is taken approximately halfway between P and C for spherical mirrors under the usual paraxial approximation. Thus R ≈ 2f in the practical ray-optics treatment.

22. Diagram Labelling Practice

Students should label:

1. P → Pole
2. F → Principal Focus
3. C → Centre of Curvature
4. PC → Radius of Curvature
5. PF → Focal Length
6. P–C line → Principal Axis

23. CBSE Golden Points ⭐

• Spherical mirror is a part of a hollow sphere.
• There are two types: concave and convex.
• P = Pole.
• C = Centre of curvature.
• F = Principal focus.
• R = Radius of curvature = PC.
• f = Focal length = PF.
• Principal axis passes through P and C.
• For a concave mirror, F and C are in front of the mirror.
• For a convex mirror, F and C are behind the mirror.
• F lies approximately midway between P and C.
• R = 2f.
• For a concave mirror, parallel rays converge at F.
• For a convex mirror, parallel rays appear to diverge from F.
• A ray directed through C strikes the spherical surface normally.
• Aperture represents the effective diameter/width of the reflecting surface.
• Distances in mirror problems are measured from P.

24. Memory Tricks 🧠

P – F – C Memory:

P → F → C
Pole → Focus → Centre of Curvature

For a concave mirror, these points are arranged in front of the mirror from mirror outward as: P – F – C

Distance Trick:

PF = f
PC = R
R = 2f

Mirror Trick:

Concave → F & C in Front
Convex → F & C Behind

25. One-Line Revision

P = Pole | F = Focus | C = Centre of Curvature

R = PC

f = PF

R = 2f

Principal Axis = Line through P and C

Concave → Converging | Convex → Diverging

26. Final Summary | अंतिम सारांश

The basic terms related to spherical mirrors are essential for understanding ray diagrams and numerical problems.

Pole (P): Geometrical centre of the reflecting surface.

Centre of Curvature (C): Centre of the sphere of which the mirror is a part.

Radius of Curvature (R): Distance PC.

Principal Axis: Line passing through P and C.

Principal Focus (F): Point associated with convergence or apparent divergence of rays parallel to the principal axis.

Focal Length (f): Distance PF.

Aperture: Effective diameter/width of the reflecting surface.

Most important relation:

R = 2f

Understanding these terms makes the construction of spherical-mirror ray diagrams and the solution of numerical problems much easier.

🪞 Terms Related to Spherical Mirrors

Class 10 Science | Light – Reflection and Refraction

P → F → C | R = PC | f = PF | R = 2f

Class 10th Science Chapter 9 – Light – Reflection and Refraction | Concave and Convex Mirrors

🪞 Light – Reflection and Refraction | Concave and Convex Mirrors

Class 10 Science | CBSE + Foundation + Competitive Level

🪞 Concave and Convex Mirrors | अवतल एवं उत्तल दर्पण

1. Introduction | परिचय

Concave and convex mirrors are two types of spherical mirrors.

A spherical mirror is a reflecting surface that forms a part of a hollow sphere.

गोलीय दर्पण वह परावर्तक सतह है जो किसी खोखले गोले के एक भाग के रूप में बनी होती है।

Concave Mirror Convex Mirror

2. Concave Mirror | अवतल दर्पण

A concave mirror has its reflecting surface curved inward.

It is called a converging mirror because parallel rays of light converge after reflection.

अवतल दर्पण की परावर्तक सतह अंदर की ओर मुड़ी होती है। यह प्रकाश की समानांतर किरणों को परावर्तन के बाद अभिसरित करता है।

3. Convex Mirror | उत्तल दर्पण

A convex mirror has its reflecting surface curved outward.

It is called a diverging mirror because parallel rays diverge after reflection.

उत्तल दर्पण की परावर्तक सतह बाहर की ओर उभरी होती है। यह परावर्तन के बाद प्रकाश किरणों को अपसरित करता है।

4. Concave vs Convex Mirror

Property	Concave Mirror	Convex Mirror
Reflecting surface	Curved inward	Curved outward
Nature	Converging	Diverging
Focus	In front of mirror	Behind mirror
Image	Real or virtual	Always virtual for a real object
Image size	Diminished, same or enlarged	Always diminished
Common use	Shaving mirror, headlights	Rear-view mirror

5. Important Parts of Both Mirrors

Term	Symbol	Meaning
Pole	P	Centre of the reflecting surface
Centre of Curvature	C	Centre of the sphere of which mirror is a part
Radius of Curvature	R	Distance PC
Principal Focus	F	Point related to convergence/divergence of parallel rays
Focal Length	f	Distance PF
Principal Axis	—	Line passing through P and C

6. Relation Between Radius of Curvature and Focal Length

R = 2f

f = R/2

For a spherical mirror, under the usual paraxial approximation, the principal focus lies approximately halfway between P and C.

इसलिए:
PF = FC
और
PC = 2PF

7. Ray Rules – Concave Mirror

Incident Ray	Reflected Ray
Parallel to principal axis	Passes through F
Passing through F	Becomes parallel to principal axis
Passing through C	Retraces its path
Striking pole P	Reflects according to i = r

8. Ray Rules – Convex Mirror

Incident Ray	Reflected Ray
Parallel to principal axis	Appears to diverge from F behind mirror
Directed towards F behind mirror	Reflects parallel to principal axis
Directed towards C behind mirror	Retraces its path

9. Image Formation by Concave Mirror

Object Position	Image Position	Nature	Size
At infinity	At F	Real and inverted	Highly diminished
Beyond C	Between C and F	Real and inverted	Diminished
At C	At C	Real and inverted	Same size
Between C and F	Beyond C	Real and inverted	Enlarged
At F	At infinity	Real and inverted	Highly enlarged
Between F and P	Behind mirror	Virtual and erect	Enlarged

10. Image Formation by Convex Mirror

For a real object placed anywhere in front of a convex mirror, the image is always:

Virtual + Erect + Diminished

and is formed behind the mirror between P and F.

Object Position	Image Position	Nature	Size
At infinity	At F behind mirror	Virtual and erect	Highly diminished
At finite distance	Between P and F	Virtual and erect	Diminished

11. Mirror Formula

1/f = 1/v + 1/u

f = focal length
u = object distance
v = image distance

12. Magnification

m = hᵢ/hₒ = −v/u

Value of m	Interpretation
m > 1	Magnified image
m = 1	Same size image
m < 1	Diminished image
m > 0	Virtual and erect
m < 0	Real and inverted

13. New Cartesian Sign Convention

• All distances are measured from the pole P.
• Distances measured in the direction of incident light are positive.
• Distances measured opposite to the direction of incident light are negative.
• Heights above the principal axis are positive.
• Heights below the principal axis are negative.

Usual diagram arrangement:

Light travels from left to right.
For a concave mirror, C and F are generally on the left, so their distances are negative.
For a convex mirror, C and F are behind the mirror, so their distances are positive.

14. Uses of Concave Mirror

• Shaving mirrors
• Make-up mirrors
• Vehicle headlights
• Torches
• Searchlights
• Solar furnaces
• Reflecting telescopes

15. Uses of Convex Mirror

• Rear-view mirrors of vehicles
• Security mirrors in shops
• Road intersections
• Parking areas
• Large-area surveillance mirrors

16. Why is Convex Mirror Used as Rear-View Mirror?

A convex mirror is preferred because:

• It gives a wider field of view.
• It forms an erect image.
• It forms a diminished image.
• It allows the driver to see a larger region behind the vehicle.

Memory Trick: V-E-D
Virtual + Erect + Diminished

17. Why is Concave Mirror Used as a Shaving Mirror?

When the face is placed between the pole and principal focus of a concave mirror, the mirror forms a:

Virtual + Erect + Enlarged image.

Therefore, facial details appear larger and easier to see.

18. Animated Ray Diagram – Concave Mirror

19. 30 MCQs | Multiple Choice Questions

Q1. Which mirror has a reflecting surface curved inward?

A. Concave mirror

B. Convex mirror

C. Plane mirror

D. Cylindrical mirror

Answer: A

Q2. A convex mirror is known as a:

A. Converging mirror

B. Diverging mirror

C. Plane mirror

D. Focusing mirror

Answer: B

Q3. A concave mirror is called a:

A. Diverging mirror

B. Plane mirror

C. Converging mirror

D. Transparent mirror

Answer: C

Q4. The centre of the sphere of which a mirror is a part is called:

A. Pole

B. Focus

C. Vertex

D. Centre of curvature

Answer: D

Q5. The distance PC represents:

A. Radius of curvature

B. Focal length

C. Object distance

D. Image distance

Answer: A

Q6. The distance PF represents:

A. Diameter

B. Focal length

C. Radius

D. Object height

Answer: B

Q7. For a spherical mirror, the relation between R and f is:

A. R = f

B. R = f/2

C. R = 2f

D. R = 4f

Answer: C

Q8. A ray parallel to the principal axis of a concave mirror passes through:

A. P

B. C

C. Infinity

D. F

Answer: D

Q9. A ray passing through C of a concave mirror:

A. Retraces its path

B. Becomes parallel

C. Passes through P

D. Goes to infinity

Answer: A

Q10. A convex mirror forms an image that is always:

A. Real and inverted

B. Virtual and erect

C. Real and enlarged

D. Inverted and enlarged

Answer: B

Q11. A convex mirror always forms an image that is:

A. Enlarged

B. Same size

C. Diminished

D. Inverted

Answer: C

Q12. If an object is placed at C of a concave mirror, the image is:

A. At F

B. Behind mirror

C. At infinity

D. At C and same size

Answer: D

Q13. An object beyond C of a concave mirror produces an image:

A. Between C and F

B. Behind mirror

C. At P

D. At infinity

Answer: A

Q14. If an object is between C and F, the image is:

A. Between P and F

B. Beyond C

C. At C

D. Behind mirror

Answer: B

Q15. An object placed at F of a concave mirror forms an image at:

A. C

B. P

C. Infinity

D. Between F and P

Answer: C

Q16. An object placed between F and P of a concave mirror forms:

A. Real and inverted image

B. Real and diminished image

C. Real and same-size image

D. Virtual, erect and enlarged image

Answer: D

Q17. Which mirror is commonly used in vehicle rear-view mirrors?

A. Convex mirror

B. Concave mirror

C. Plane mirror

D. None

Answer: A

Q18. Which mirror is suitable for a shaving mirror?

A. Convex

B. Concave

C. Plane

D. None

Answer: B

Q19. Mirror formula is:

A. 1/f = 1/u − 1/v

B. f = u + v

C. 1/f = 1/v + 1/u

D. f = uv

Answer: C

Q20. Magnification of a spherical mirror is:

A. m = u/v

B. m = uv

C. m = u + v

D. m = −v/u

Answer: D

Q21. If R = 40 cm, then f is:

A. 20 cm

B. 40 cm

C. 80 cm

D. 10 cm

Answer: A

Q22. A concave mirror with f = −15 cm has R equal to:

A. +30 cm

B. −30 cm

C. −7.5 cm

D. +7.5 cm

Answer: B

Q23. Which mirror provides a wider field of view?

A. Concave

B. Plane

C. Convex

D. All same

Answer: C

Q24. A positive magnification generally indicates:

A. Inverted image

B. Real image

C. Diminished image only

D. Erect image

Answer: D

Q25. Which mirror can produce a magnified virtual image?

A. Concave mirror

B. Convex mirror

C. Plane mirror

D. None

Answer: A

Q26. Which mirror always forms a diminished image for a real object?

A. Concave

B. Convex

C. Plane

D. None

Answer: B

Q27. The principal focus of a convex mirror lies:

A. In front of mirror

B. At P

C. Behind mirror

D. At C in front

Answer: C

Q28. A ray incident normally on a spherical mirror is reflected:

A. At 90°

B. Parallel to axis

C. Towards F always

D. Back along the same path

Answer: D

Q29. If magnification is −2, the image is:

A. Real, inverted and twice the size

B. Virtual and half size

C. Erect and twice size

D. Same size

Answer: A

Q30. The principal axis passes through:

A. F only

B. P and C

C. C only

D. P only

Answer: B

20. 30 Subjective Questions with Answers

2 Marks Q1. What is a concave mirror?

A concave mirror is a spherical mirror whose reflecting surface is curved inward.

2 Marks Q2. What is a convex mirror?

A convex mirror is a spherical mirror whose reflecting surface is curved outward.

2 Marks Q3. Why is a concave mirror called a converging mirror?

It converges parallel rays of light towards its principal focus after reflection.

2 Marks Q4. Why is a convex mirror called a diverging mirror?

It causes parallel rays of light to diverge after reflection.

2 Marks Q5. Define focal length.

The distance between the pole and principal focus of a spherical mirror is called its focal length.

3 Marks Q6. Define pole, focus and centre of curvature.

Pole is the centre of the reflecting surface. Focus is the point related to convergence or apparent divergence of parallel rays. Centre of curvature is the centre of the sphere of which the mirror is a part.

3 Marks Q7. What is radius of curvature?

The distance between the pole P and centre of curvature C is called radius of curvature.
R = PC

3 Marks Q8. Write the relation between R and f.

R = 2f

3 Marks Q9. Write three differences between concave and convex mirrors.

Concave is inward and converging; convex is outward and diverging. Concave can form real or virtual images; convex forms a virtual image for a real object. Convex always gives a diminished image.

3 Marks Q10. State the mirror formula.

1/f = 1/v + 1/u

4 Marks Q11. State four ray rules for a concave mirror.

• Parallel ray passes through F.
• Ray through F becomes parallel.
• Ray through C retraces its path.
• Ray striking P obeys i = r.

4 Marks Q12. State the characteristics of an image formed by a convex mirror.

The image is virtual, erect and diminished and is formed behind the mirror between P and F.

4 Marks Q13. Why is a convex mirror used as a rear-view mirror?

It provides a wide field of view and forms a virtual, erect and diminished image.

4 Marks Q14. Write four uses of a concave mirror.

Shaving mirrors, headlights, torches and solar furnaces are common applications.

4 Marks Q15. Write the formula for magnification.

m = hᵢ/hₒ = −v/u

5 Marks Q16. Explain image formation by a concave mirror when the object is beyond C.

The image forms between C and F. It is real, inverted and smaller than the object.

5 Marks Q17. Explain image formation when the object is at C.

The image forms at C. It is real, inverted and of the same size as the object.

5 Marks Q18. Explain image formation when the object is between C and F.

The image is formed beyond C. It is real, inverted and enlarged.

5 Marks Q19. Explain image formation when the object is between F and P.

The image forms behind the mirror. It is virtual, erect and enlarged.

5 Marks Q20. Explain image formation by a convex mirror.

For a real object, reflected rays diverge and their backward extensions meet behind the mirror. Hence the image is always virtual, erect and diminished.

6 Marks Q21. Explain all six cases of image formation by a concave mirror.

Object	Image	Nature
Infinity	F	Real, inverted, highly diminished
Beyond C	Between C and F	Real, inverted, diminished
C	C	Real, inverted, same size
C–F	Beyond C	Real, inverted, enlarged
F	Infinity	Real, inverted, highly enlarged
F–P	Behind mirror	Virtual, erect, enlarged

6 Marks Q22. Explain the New Cartesian Sign Convention.

All distances are measured from P. Distances in the direction of incident light are positive, while those opposite to it are negative. Heights above the principal axis are positive and heights below it are negative.

6 Marks Q23. Explain why a concave mirror can form both real and virtual images.

When the object is outside F, reflected rays can actually meet to form a real image. When the object is between F and P, reflected rays diverge and their backward extensions meet behind the mirror, forming a virtual image.

6 Marks Q24. Explain the importance of the focus and centre of curvature in ray diagrams.

F and C are reference points used to construct reflected rays and determine image position, size and nature. Rays parallel to the principal axis are related to F, while a ray through C retraces its path.

6 Marks Q25. Why does a convex mirror provide a wider field of view?

Its outward-curved surface causes reflected rays to diverge, allowing light from a wider angular region to reach the observer. Therefore a larger area behind the vehicle can be seen.

6 Marks Q26. A concave mirror has focal length 20 cm. Find its radius of curvature.

R = 2f
R = 2 × 20
R = 40 cm

6 Marks Q27. A concave mirror has f = −15 cm and u = −30 cm. Find v.

Using:
1/f = 1/v + 1/u

−1/15 = 1/v − 1/30

1/v = −1/30
v = −30 cm

The image forms at C.

6 Marks Q28. A convex mirror has f = +20 cm and u = −40 cm. Find v.

1/20 = 1/v − 1/40

1/v = 3/40
v ≈ +13.33 cm

The positive sign shows that the image is behind the mirror.

6 Marks Q29. An object 4 cm high produces an image 8 cm high. Find magnification.

m = hᵢ/hₒ
m = 8/4
m = 2

The image is twice the height of the object. A positive sign, if applicable, indicates an erect image.

6 Marks Q30. An object is placed at the centre of curvature of a concave mirror. Describe the image.

The image is formed at C itself. It is real, inverted and of the same size as the object. Magnification is −1.

21. Assertion–Reason Questions

Q1. Assertion: A concave mirror can form both real and virtual images.
Reason: The nature of the image depends on the object position relative to F and P.

Answer: Both Assertion and Reason are true, and Reason correctly explains the Assertion.

Q2. Assertion: A convex mirror is used as a rear-view mirror.
Reason: A convex mirror gives a wide field of view.

Answer: Both are true and the Reason correctly explains the Assertion.

Q3. Assertion: A ray passing through C of a concave mirror retraces its path.
Reason: It strikes the mirror normally.

Answer: Both are true and the Reason correctly explains the Assertion.

Q4. Assertion: A convex mirror always forms a diminished image for a real object.
Reason: It is a diverging mirror.

Answer: Both are true and the Reason correctly explains the Assertion.

Q5. Assertion: An object at C of a concave mirror produces an image at C.
Reason: A ray through C retraces its path.

Answer: Both are true, but the Reason alone is not the complete explanation of the image formation.

22. HOTS | Higher Order Thinking

HOTS 1: Why can a concave mirror be used both as a shaving mirror and as a reflector in headlights?

Its behaviour depends on the object/ray arrangement. It can form a magnified virtual image for an object between P and F and can produce a parallel beam when a source is placed near F.

HOTS 2: Why is a convex mirror safer for rear-view applications?

It provides a wider field of view and gives an erect image, allowing the driver to observe a larger region behind the vehicle.

HOTS 3: What happens to the image if an object moves from beyond C towards F in front of a concave mirror?

The image moves from between C and F towards beyond C and becomes progressively larger.

HOTS 4: What happens when an object is exactly at F of a concave mirror?

Reflected rays become parallel to the principal axis, so the image is considered to be at infinity and is highly enlarged.

HOTS 5: A mirror forms a virtual, erect and enlarged image. Identify the mirror and object position.

It is a concave mirror, with the object placed between P and F.

23. Diagram Labelling Practice

Important Labels:

P → Pole
F → Principal Focus
C → Centre of Curvature
PC → Radius of Curvature
PF → Focal Length
P–F–C → Principal Axis

24. CBSE Golden Points ⭐

• Concave mirror = converging mirror.
• Convex mirror = diverging mirror.
• Concave reflecting surface is inward.
• Convex reflecting surface is outward.
• P = Pole.
• F = Principal focus.
• C = Centre of curvature.
• R = PC.
• f = PF.
• R = 2f.
• Concave mirror can form real and virtual images.
• Convex mirror forms virtual, erect and diminished image for a real object.
• Convex mirror provides a wider field of view.
• Concave mirror can produce a magnified virtual image.
• Mirror formula: 1/f = 1/v + 1/u.
• Magnification: m = −v/u.
• Positive magnification means erect image.
• Negative magnification means inverted image.
• Ray through C retraces its path.
• Correct sign convention is essential for numerical problems.

25. Memory Tricks 🧠

Mirror Type:

CONCAVE → CONVERGE
CONVEX → DIVERGE

Convex Mirror Image:

V – E – D
Virtual → Erect → Diminished

Important Points:

P → F → C
Pole → Focus → Centre of Curvature

Formula:

R = 2f
Radius = Twice focal length

Concave Mirror Sequence:

∞ → F
Beyond C → C–F
C → C
C–F → Beyond C
F → ∞
F–P → Behind Mirror

26. One-Line Revision

Concave = Converging | Convex = Diverging

R = 2f

1/f = 1/v + 1/u

m = hᵢ/hₒ = −v/u

Convex Mirror → Virtual + Erect + Diminished

27. Final Summary | अंतिम सारांश

Concave and convex mirrors are important applications of reflection of light.

Concave mirror:
Inward curved, converging and capable of producing different types of images depending on object position.

Convex mirror:
Outward curved, diverging and always produces a virtual, erect and diminished image for a real object.

The most important quantities are: P, F, C, R and f.

The key formulas are:

R = 2f

1/f = 1/v + 1/u

m = hᵢ/hₒ = −v/u

Exam Tip: Always draw a neat ray diagram and apply the correct New Cartesian Sign Convention before solving numerical problems.

🪞 Concave & Convex Mirrors

Class 10 Science | Light – Reflection and Refraction

Concept → Ray Diagram → Image Formation → Formula → Numerical → Practice