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

🪞 Light – Reflection and Refraction | Spherical Mirrors

Class 10 Science | CBSE + Foundation + Competitive Level

🪞 Spherical Mirrors | गोलीय दर्पण

1. Introduction to Spherical Mirrors | गोलीय दर्पण का परिचय

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

गोलीय दर्पण: ऐसा परावर्तक दर्पण जिसकी परावर्तक सतह किसी खोखले गोले के एक भाग के रूप में होती है, गोलीय दर्पण कहलाता है।

Spherical mirrors are mainly of two types:

Concave Mirror Convex Mirror

2. Types of Spherical Mirrors | गोलीय दर्पण के प्रकार

Concave Mirror	Convex Mirror
Reflecting surface is curved inward. परावर्तक सतह अंदर की ओर मुड़ी होती है।	Reflecting surface is curved outward. परावर्तक सतह बाहर की ओर उभरी होती है।
Also called converging mirror.	Also called diverging mirror.
Can form real or virtual images depending on object position.	For a real object, it forms a virtual, erect and diminished image.

3. Concave Mirror | अवतल दर्पण

A concave mirror has its reflecting surface on the inner side of the spherical surface.

Its reflecting surface faces the centre of curvature.

अवतल दर्पण की परावर्तक सतह गोलीय सतह के अंदर की ओर होती है।

4. Convex Mirror | उत्तल दर्पण

A convex mirror has its reflecting surface on the outer side of the spherical surface.

It causes parallel rays to diverge after reflection.

उत्तल दर्पण की परावर्तक सतह बाहर की ओर उभरी होती है।

5. Important Terms of Spherical Mirrors

Term	Definition	Hindi
Pole (P)	Centre of reflecting surface of the mirror	ध्रुव
Centre of Curvature (C)	Centre of the sphere of which mirror is a part	वक्रता केन्द्र
Radius of Curvature (R)	Distance between P and C	वक्रता त्रिज्या
Principal Axis	Straight line passing through P and C	मुख्य अक्ष
Principal Focus (F)	Point where parallel rays converge or appear to diverge from after reflection	मुख्य फोकस
Focal Length (f)	Distance between P and F	फोकस दूरी

6. Pole (P) | ध्रुव

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

गोलीय दर्पण की परावर्तक सतह के ज्यामितीय केन्द्र को ध्रुव (P) कहते हैं।

7. Centre of Curvature (C) | वक्रता केन्द्र

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

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

8. Radius of Curvature (R) | वक्रता त्रिज्या

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

R = PC

9. Principal Axis | मुख्य अक्ष

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

ध्रुव और वक्रता केन्द्र से गुजरने वाली सीधी रेखा को मुख्य अक्ष कहते हैं।

10. Principal Focus (F) | मुख्य फोकस

When rays parallel to the principal axis fall on a concave mirror, they converge at a point on the principal axis. This point is called the principal focus.

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

11. Focal Length (f) | फोकस दूरी

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

f = PF

12. Relation Between R and f

R = 2f

f = R/2

For a spherical mirror under the standard paraxial approximation, the principal focus lies approximately midway between the pole and centre of curvature.

अर्थात: PF = FC और PC = 2PF

13. Sign Convention for Spherical Mirrors

Class 10 Physics uses the New Cartesian Sign Convention.

• All distances are measured from the pole.
• 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.

For the usual arrangement where light travels from left to right:

Concave mirror: C and F are generally on the left → negative distances.
Convex mirror: C and F are behind the mirror → positive distances.

14. Important Ray Rules for Concave Mirror

Ray	After Reflection
Parallel to principal axis	Passes through F
Through F	Becomes parallel to principal axis
Through C	Retraces its path
Striking pole	Obeys i = r

15. Important Ray Rules for 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	Reflects back along the same line

16. Image Formation by Concave Mirror

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

17. Image Formation by Convex Mirror

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

Virtual Erect Diminished Behind Mirror

Object Position	Image Position
At infinity	At F behind mirror
Finite distance	Between P and F behind mirror

18. Animated Concave Mirror Ray Diagram

19. Mirror Formula

1/f = 1/v + 1/u

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

20. Magnification

m = hᵢ / hₒ = −v/u

Where:
hᵢ = image height
hₒ = object height
u = object distance
v = image distance

Magnification	Meaning
m > 1	Magnified image
m = 1	Same size
m < 1	Diminished image
m positive	Virtual and erect image
m negative	Real and inverted image

21. Uses of Concave Mirror

• Shaving and makeup mirrors
• Reflectors in torches
• Vehicle headlights
• Searchlights
• Solar furnaces
• Reflecting telescopes

A concave mirror can produce a magnified upright image when the object is placed between the pole and focus.

22. Uses of Convex Mirror

• Rear-view mirrors in vehicles
• Security mirrors in shops
• Mirrors at road intersections
• Parking-area mirrors

Why convex mirrors are used as rear-view mirrors?

They provide a wide field of view and always form virtual, erect and diminished images.

23. Concave vs Convex Mirror

Feature	Concave	Convex
Surface	Inward curved	Outward curved
Nature	Converging	Diverging
Focus	In front of mirror	Behind mirror
Image	Real/virtual depending on object position	Always virtual for real object
Size	May be enlarged, same or diminished	Always diminished
Common Use	Shaving mirror, headlight	Rear-view mirror

24. 30 MCQs | Multiple Choice Questions

Q1. A spherical mirror is a part of:

A. A hollow sphere

B. A cylinder

C. A plane

D. A cone

Answer: A

Q2. A concave mirror has its reflecting surface:

A. Outward

B. Inward

C. Plane

D. Both sides equally

Answer: B

Q3. A convex mirror is also called a:

A. Converging mirror

B. Plane mirror

C. Diverging mirror

D. Cylindrical 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 is called:

A. Radius of curvature

B. Focal length

C. Object distance

D. Image distance

Answer: A

Q6. The distance PF is called:

A. Radius

B. Focal length

C. Diameter

D. Object distance

Answer: B

Q7. The relation between R and f is:

A. R = f

B. R = f/2

C. R = 2f

D. R = 4f

Answer: C

Q8. The principal axis passes through:

A. F only

B. C only

C. P only

D. P and C

Answer: D

Q9. Parallel rays incident on a concave mirror converge at:

A. F

B. P

C. C

D. Infinity

Answer: A

Q10. Parallel rays incident on a convex mirror appear to diverge from:

A. C in front

B. F behind the mirror

C. P

D. Infinity

Answer: B

Q11. An object at C of a concave mirror forms an image:

A. At F

B. Behind mirror

C. At C

D. At P

Answer: C

Q12. An object at C produces an image that is:

A. Virtual and erect

B. Enlarged

C. Diminished

D. Real, inverted and same size

Answer: D

Q13. If an object is placed beyond C of a concave mirror, image forms:

A. Between C and F

B. Beyond C

C. Behind mirror

D. At P

Answer: A

Q14. An object between C and F of a concave mirror forms an image:

A. Between P and F

B. Beyond C

C. At F

D. Behind mirror

Answer: B

Q15. When an object is placed at F of a concave mirror, image forms:

A. At C

B. At P

C. At infinity

D. Behind mirror

Answer: C

Q16. When an object is between F and P of a concave mirror, image is:

A. Real and inverted

B. Real and diminished

C. Real and same size

D. Virtual, erect and enlarged

Answer: D

Q17. A convex mirror always forms a real image for a real object.

A. False

B. True

C. Only at infinity

D. Only at C

Answer: A

Q18. The image formed by a convex mirror is always:

A. Real, inverted and enlarged

B. Virtual, erect and diminished

C. Real and same size

D. Inverted and enlarged

Answer: B

Q19. Which mirror is commonly used as a rear-view mirror?

A. Plane

B. Concave

C. Convex

D. Cylindrical

Answer: C

Q20. Mirror formula is:

A. 1/f = 1/u − 1/v

B. f = u + v

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

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

Answer: D

Q21. Magnification for a spherical mirror is:

A. m = −v/u

B. m = u/v

C. m = uv

D. m = u + v

Answer: A

Q22. If f = −10 cm for a concave mirror, then its radius is:

A. +20 cm

B. −20 cm

C. −5 cm

D. +5 cm

Answer: B

Q23. A convex mirror has focal length:

A. Always zero

B. Always negative

C. Positive under Cartesian convention

D. Infinite

Answer: C

Q24. A ray passing through C of a concave mirror:

A. Becomes parallel

B. Goes through F

C. Diverges completely

D. Retraces its path

Answer: D

Q25. Which mirror can be used as a shaving mirror?

A. Concave mirror

B. Convex mirror

C. Plane glass

D. Convex lens only

Answer: A

Q26. A concave mirror is called a:

A. Diverging mirror

B. Converging mirror

C. Plane mirror

D. Transparent mirror

Answer: B

Q27. If R = 40 cm, focal length is:

A. 40 cm

B. 80 cm

C. 20 cm

D. 10 cm

Answer: C

Q28. A positive magnification for a mirror generally indicates:

A. Real and inverted

B. Real and enlarged

C. Always diminished

D. Virtual and erect

Answer: D

Q29. Which mirror provides a wider field of view?

A. Convex mirror

B. Concave mirror

C. Plane mirror

D. All provide exactly the same

Answer: A

Q30. For a spherical mirror, the principal focus lies approximately:

A. At P

B. Midway between P and C

C. Beyond C always

D. At infinity always

Answer: B

25. 30 Subjective Questions with Answers

2 Marks Q1. What is a spherical mirror?

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

2 Marks Q2. Name the two types of spherical mirrors.

Concave mirror and convex mirror.

2 Marks Q3. Define pole of a spherical mirror.

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

2 Marks Q4. Define radius of curvature.

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

2 Marks Q5. Define focal length.

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

3 Marks Q6. Differentiate between concave and convex mirrors.

Concave mirror has an inward-curved reflecting surface and is converging. Convex mirror has an outward-curved reflecting surface and is diverging.

3 Marks Q7. What is the principal axis?

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

3 Marks Q8. What is centre of curvature?

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

3 Marks Q9. Write the relation between R and f.

For a spherical mirror:
R = 2f
or
f = R/2

3 Marks Q10. Why is a convex mirror used as a rear-view mirror?

Because it provides a wide field of view and forms a virtual, erect and diminished image of objects behind the vehicle.

4 Marks Q11. Explain pole, centre of curvature, radius of curvature and principal axis.

Pole is the centre of the reflecting surface. Centre of curvature is the centre of the sphere of which the mirror is a part. Radius of curvature is PC. Principal axis is the straight line passing through P and C.

4 Marks Q12. Explain principal focus of a concave mirror.

When rays parallel to the principal axis fall on a concave mirror, they converge at a point on the principal axis. This point is called the principal focus.

4 Marks Q13. Explain principal focus of a convex mirror.

Parallel rays incident on a convex mirror diverge after reflection. Their backward extensions meet at a point behind the mirror. This point is the principal focus.

4 Marks Q14. Write four important ray rules for a concave mirror.

• Parallel ray → passes through F.
• Ray through F → becomes parallel.
• Ray through C → retraces its path.
• Ray at pole → follows i = r.

4 Marks Q15. Write the mirror formula and magnification formula.

Mirror formula:
1/f = 1/v + 1/u

Magnification:
m = hᵢ/hₒ = −v/u

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

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

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

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

5 Marks Q18. Explain image formation when the object lies 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 lies between F and P.

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

5 Marks Q20. Write the characteristics of image formed by a convex mirror.

For a real object, the image formed by a convex mirror is always virtual, erect and diminished, and lies behind the mirror between P and F.

6 Marks Q21. Explain all six important 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
At C	At C	Real, inverted, same size
Between C and F	Beyond C	Real, inverted, enlarged
At F	Infinity	Real, inverted, highly enlarged
Between F and P	Behind mirror	Virtual, erect, enlarged

6 Marks Q22. Explain the Cartesian sign convention for spherical mirrors.

All distances are measured from the pole. Distances measured in the direction of incident light are positive, while distances measured 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 the focus, reflected rays can actually meet and form a real image. When the object is placed between F and P, reflected rays diverge and their backward extensions meet behind the mirror, producing a virtual image.

6 Marks Q24. Explain why a convex mirror always forms a virtual image for a real object.

A convex mirror causes reflected rays to diverge. The rays do not actually meet in front of the mirror; only their backward extensions meet behind the mirror. Therefore the image is virtual and erect.

6 Marks Q25. Explain the relation R = 2f.

For a spherical mirror under the paraxial approximation, the principal focus lies approximately midway between the pole and centre of curvature. Therefore:

PF = FC
PC = PF + FC = 2PF
Hence:
R = 2f

6 Marks Q26. Explain the uses of concave mirrors.

Concave mirrors are used in shaving mirrors, makeup mirrors, headlights, torches, searchlights, solar furnaces and reflecting telescopes because they can converge light and can form magnified images for suitable object positions.

6 Marks Q27. Explain the uses of convex mirrors.

Convex mirrors are used as rear-view mirrors, security mirrors and road-intersection mirrors because they form upright diminished images and provide a wider field of view.

6 Marks Q28. An object is placed 30 cm in front of a concave mirror of focal length 15 cm. Find the image position.

Given:
u = −30 cm
f = −15 cm

Mirror formula:
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, i.e. at C.

6 Marks Q29. A convex mirror has focal length 20 cm. An object is placed 40 cm in front of it. Find the image distance.

Given:
f = +20 cm
u = −40 cm

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

1/20 = 1/v − 1/40

1/v = 1/20 + 1/40
1/v = 3/40
v = 13.33 cm approximately

Positive v indicates that the image is formed behind the mirror.

6 Marks Q30. An object 5 cm high produces an image 10 cm high. Find the magnification.

Given:
hₒ = 5 cm
hᵢ = 10 cm

m = hᵢ/hₒ
m = 10/5
m = 2

The image is twice the height of the object. If m is positive, the image is virtual and erect.

26. Assertion–Reason Questions

Q1. Assertion: A concave mirror can form a real as well as a virtual image.
Reason: The image nature depends on the position of the object 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: It provides a wide field of view and forms diminished images.

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: The ray strikes the mirror normally at the point of incidence.

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

Q4. Assertion: For a spherical mirror, R = 2f.
Reason: The principal focus lies approximately midway between P and C.

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

Q5. Assertion: A convex mirror always forms a diminished image of a real object.
Reason: Reflected rays diverge and their backward extensions meet behind the mirror.

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

27. HOTS | Higher Order Thinking Questions

HOTS 1: Why is a concave mirror suitable for a shaving mirror?

When the face is placed between the pole and focus, the concave mirror forms a virtual, erect and magnified image.

HOTS 2: Why is a convex mirror preferred for vehicle rear-view mirrors instead of a concave mirror?

A convex mirror provides a wider field of view and produces a virtual, erect and diminished image, allowing the driver to see a larger region behind the vehicle.

HOTS 3: An object is placed at the focus of a concave mirror. Why is the image formed at infinity?

After reflection, rays from an object placed at F become parallel to the principal axis. Parallel rays meet only at infinity in the ideal ray-diagram sense, so the image is highly enlarged and considered to be at infinity.

HOTS 4: Why does a concave mirror sometimes form an enlarged image and sometimes a diminished image?

The image size depends on the object position. Different positions relative to C and F produce different image sizes.

HOTS 5: A mirror produces a virtual, erect and enlarged image. Which spherical mirror and object position can produce it?

A concave mirror with the object placed between its pole P and principal focus F.

28. 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 convex mirror has radius of curvature 30 cm. Find its focal length.

f = R/2
f = 30/2
f = 15 cm

Numerical 3: An object is placed 20 cm in front of a concave mirror of focal length 10 cm. Find v.

u = −20 cm
f = −10 cm

1/f = 1/v + 1/u
−1/10 = 1/v − 1/20
1/v = −1/20
v = −20 cm

Numerical 4: 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

Image is behind the mirror.

Numerical 5: An object of height 4 cm forms an image of height −8 cm. Find magnification.

m = hᵢ/hₒ
m = −8/4
m = −2

Negative sign indicates an inverted image and magnitude 2 means the image is twice the object size.

29. Diagram Labelling Practice

Labels to remember:

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

30. CBSE Golden Points ⭐

• Spherical mirrors are parts of hollow spheres.
• Concave mirror is a converging mirror.
• Convex mirror is a diverging mirror.
• P = Pole.
• C = Centre of curvature.
• F = Principal focus.
• R = PC.
• f = PF.
• For spherical mirrors, R = 2f.
• Principal axis passes through P and C.
• Concave mirror can form real or virtual images.
• Convex mirror forms virtual, erect and diminished images for real objects.
• Mirror formula: 1/f = 1/v + 1/u.
• Magnification: m = −v/u.
• Positive magnification indicates an erect image.
• Negative magnification indicates an inverted image.
• Convex mirrors are used as rear-view mirrors.
• Concave mirrors can be used as shaving mirrors.
• A ray through C of a concave mirror retraces its path.
• Always use the correct Cartesian sign convention in numericals.

31. Memory Tricks 🧠

Mirror Types:

Concave = Converge
Convex = Diverge

Important Points:

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

For a concave mirror, these points lie in front of the mirror.

Formula Trick:

R = 2f
“Radius is Twice Focus”

Concave Mirror Image Sequence:

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

Convex Mirror:

V-E-D
Virtual + Erect + Diminished

32. One-Line Revision

Spherical Mirror = Part of a Hollow Sphere

Concave → Converging | Convex → Diverging

R = 2f

1/f = 1/v + 1/u

m = hᵢ/hₒ = −v/u

33. Final Summary | अंतिम सारांश

Spherical mirrors are important reflecting optical devices.

There are two major types: Concave Mirror and Convex Mirror.

A concave mirror can form different types of images depending on the position of the object. It can produce real, inverted images as well as virtual, erect and enlarged images.

A convex mirror produces a virtual, erect and diminished image for a real object and provides a wide field of view.

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

The key relations are:

R = 2f

1/f = 1/v + 1/u

m = hᵢ/hₒ = −v/u

For Class 10 numerical problems, the correct application of the New Cartesian Sign Convention is essential.

🪞 Spherical Mirrors

Class 10 Science | Light – Reflection and Refraction

Concept → Ray Diagram → Formula → Numerical → Practice