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