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