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