Light-Reflection and Refraction: Class 10 Science answers, notes

Summary

We see things because light bounces off them and enters our eyes. This bouncing is called reflection. Light usually travels in straight paths. When light hits a smooth surface like a mirror, it follows certain rules. The angle at which light hits the surface is the same as the angle at which it bounces off.

Flat mirrors, known as plane mirrors, create images that are upright and the same size as the object. These images appear behind the mirror. They are called virtual, which means they cannot be formed on a screen. These images are also flipped left to right.

Curved mirrors are called spherical mirrors. A concave mirror curves inwards, like the inside of a spoon. It can form different kinds of images. Sometimes the image is real, meaning it can be projected onto a screen, and it might be upside down. Other times, the image is virtual and upright. Concave mirrors are used in torches. A convex mirror curves outwards, like the back of a spoon. It always forms images that are virtual, upright, and smaller than the object. Cars use convex mirrors as side-view mirrors because they offer a wider view.

Spherical mirrors have a few important points: the pole (the center of the mirror’s surface), the center of curvature (the center of the sphere from which the mirror is a part), the principal axis (a line passing through the pole and center of curvature), and the principal focus (a point where parallel light rays meet or appear to meet after reflection). The distance from the pole to the principal focus is the focal length. A formula, 1/v + 1/u = 1/f, connects the object distance (u), the image distance (v), and the focal length (f). Magnification tells us if the image is larger or smaller than the object.

Light also bends when it travels from one material to another, for example, from air to water. This bending is called refraction. Refraction occurs because the speed of light changes as it moves through different materials. When light enters a denser material where it slows down, it bends towards an imaginary line perpendicular to the surface. When it enters a less dense material where it speeds up, it bends away from this line. This is why a straw in a glass of water appears bent.

Lenses also work because of refraction. A convex lens is thicker in the middle and causes light rays to come together, or converge. It can form both real and virtual images. A concave lens is thinner in the middle and causes light rays to spread out, or diverge. It always forms images that are virtual, upright, and smaller. Lenses also have a principal focus and a focal length. The lens formula is 1/v – 1/u = 1/f. The power of a lens indicates how much it can bend light. The unit for the power of a lens is the dioptre.

Textbook solutions

Intext Questions and Answers I

1. Define the principal focus of a concave mirror.

Answer: When a number of rays parallel to the principal axis are falling on a concave mirror, the reflected rays meet/intersect at a point on the principal axis of the mirror. This point is called the principal focus of the concave mirror.

2. The radius of curvature of a spherical mirror is 20 cm. What is its focal length?

Answer: For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length. This is expressed as R = 2f.

Radius of curvature (R) = 20 cm

Focal length (f) = R/2
= 20 cm / 2
= 10 cm

3. Name a mirror that can give an erect and enlarged image of an object.

Answer: A concave mirror can give an erect and enlarged image of an object when the object is placed between the pole (P) and the principal focus (F) of the mirror.

4. Why do we prefer a convex mirror as a rear-view mirror in vehicles?

Answer: Convex mirrors are preferred as rear-view mirrors in vehicles because they always give an erect, though diminished, image. Also, they have a wider field of view as they are curved outwards. Thus, convex mirrors enable the driver to view a much larger area than would be possible with a plane mirror.

Intext Questions and Answers II

1. Find the focal length of a convex mirror whose radius of curvature is 32 cm.

Answer: Relation between radius of curvature and focal length of a spherical mirror: R = 2 f

Given R = 32 cm,

∴ f = R / 2
= 32 cm / 2
= 16 cm.

As the mirror is convex, f is taken as positive: f = +16 cm

2. A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?

Answer: Magnification produced by a spherical mirror: m = – v / u

For a three-times enlarged real image, m = –3 (real ⇒ inverted ⇒ negative magnification).
Object distance (u) = –10 cm (by convention, real object distances are negative).

Substitute into m formula:
∴ –3 = – v / (–10)
⇒ –3 = v / 10
⇒ v = –30 cm

The negative sign for v indicates the image lies on the same side as the object (in front of the mirror), and is real and inverted.

Location of image: 30 cm in front of the concave mirror.

Intext Questions and Answers III

1. A ray of light travelling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal? Why?

Answer: When a ray of light travels from a rarer medium to a denser medium, it slows down and bends towards the normal. Since water is optically denser than air, a ray of light travelling in air that enters obliquely into water will bend towards the normal.

2. Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3 x 10⁸ m s⁻¹.

Answer: v = c / n

Here, c = 3 × 10⁸ m s⁻¹ (speed of light in vacuum)
n = 1.50 (refractive index of glass)

Substitute the known values:
v = (3 × 10⁸ m s⁻¹) / 1.50
⇒ v = 3 × 10⁸ m s⁻¹ / 1.5
⇒ v = 2 × 10⁸ m s⁻¹

3. Find out, from Table 9.3, the medium having highest optical density. Also find the medium with lowest optical density.

Material Medium	Refractive Index
Air	1.0003
Ice	1.31
Water	1.33
Alcohol	1.36
Kerosene	1.44
Fused quartz	1.46
Turpentine oil	1.47
Benzene	1.50
Crown glass	1.52
Canada Balsam	1.53
Rock salt	1.54
Carbon disulphide	1.63
Dense flint glass	1.65
Ruby	1.71
Sapphire	1.77
Diamond	2.42

Answer: From Table 9.3, the medium having the highest optical density is Diamond, with a refractive index of 2.42. The medium with the lowest optical density listed in Table 9.3 is Air, with a refractive index of 1.0003.

4. You are given kerosene, turpentine and water. In which of these does the light travel fastest? Use the information given in Table 9.3.

Answer: According to Table 9.3, the refractive indices are:

Water: 1.33
Kerosene: 1.44
Turpentine oil: 1.47

The speed of light is higher in a rarer medium, which has a lower refractive index. Comparing the refractive indices, water has the lowest refractive index (1.33). Therefore, light travels fastest in water among the given substances.

5. The refractive index of diamond is 2.42. What is the meaning of this statement?

Answer: The statement that the refractive index of diamond is 2.42 means that the ratio of the speed of light in air (or vacuum) to the speed of light in diamond is equal to 2.42.

Intext Questions and Answers IV

1. Define 1 dioptre of power of a lens.

Answer: 1 dioptre is the power of a lens whose focal length is 1 metre. The SI unit of power of a lens is ‘dioptre’, and it is denoted by the letter D.

2. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

Answer: m = –1
⇒ – v / u = –1
⇒ v / u = 1
⇒ v = u

v = 50 cm (real image distance).
∴ u = 50 cm

1 / f = 1 / v + 1 / u
⇒ 1 / f = 1 / 50 + 1 / 50
⇒ 1 /f = 2 / 50
⇒ 1 / f = 1 / 25

∴ f = 25 cm

P = 1 / f (in metres)
⇒ P = 1 / 0.25 m
⇒ P = +4 D

The needle must be placed 50 cm in front of the convex lens. The power of the lens is +4 D.

3. Find the power of a concave lens of focal length 2 m.

Answer: The power of a lens be given by: P = 1 / f (in metres)

Here,
f = – 2 m

P = 1 / (– 2)
⇒ P = – 0.5 dioptres

Exercise Questions and Answers

1. Which one of the following materials cannot be used to make a lens?

(a) Water
(b) Glass
(c) Plastic
(d) Clay

Answer: (d) Clay

2. The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?

(a) Between the principal focus and the centre of curvature
(b) At the centre of curvature
(c) Beyond the centre of curvature
(d) Between the pole of the mirror and its principal focus.

Answer: (d) Between the pole of the mirror and its principal focus.

3. Where should an object be placed in front of a convex lens to get a real image of the size of the object?

(a) At the principal focus of the lens
(b) At twice the focal length
(c) At infinity
(d) Between the optical centre of the lens and its principal focus.

Answer: (b) At twice the focal length

4. A spherical mirror and a thin spherical lens have each a focal length of -15 cm. The mirror and the lens are likely to be

(a) both concave.
(b) both convex.
(c) the mirror is concave and the lens is convex.
(d) the mirror is convex, but the lens is concave.

Answer: (a) both concave.

5. No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be

(a) only plane.
(b) only concave.
(c) only convex.
(d) either plane or convex.

Answer: (d) either plane or convex.

6. Which of the following lenses would you prefer to use while reading small letters found in a dictionary?

(a) A convex lens of focal length 50 cm.
(b) A concave lens of focal length 50 cm.
(c) A convex lens of focal length 5 cm.
(d) A concave lens of focal length 5 cm.

Answer: (c) A convex lens of focal length 5 cm.

7. We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.

Answer: To obtain an erect image using a concave mirror of focal length 15 cm, the object should be placed at a distance less than 15 cm from the mirror, i.e., between the pole (P) and the principal focus (F) of the mirror.

The nature of the image formed will be virtual and erect.

The image will be larger than the object (enlarged).

8. Name the type of mirror used in the following situations. (a) Headlights of a car. (b) Side/rear-view mirror of a vehicle. (c) Solar furnace. Support your answer with reason.

Answer: (a) Headlights of a car: Concave mirrors are used.

Reason: Concave mirrors are used in vehicle headlights to get powerful parallel beams of light when the light source is placed at their principal focus.

(b) Side/rear-view mirror of a vehicle: Convex mirrors are used.

Reason: Convex mirrors are preferred because they always give an erect, though diminished, image. Also, they have a wider field of view as they are curved outwards, enabling the driver to view a much larger area of the traffic behind him/her to facilitate safe driving.

Reason: Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces. The sunlight is converged at the focus of the mirror, producing a high temperature.

9. One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations.

Answer: Yes, if one-half of a convex lens is covered with a black paper, the lens will still produce a complete image of the object.

Explanation: Each small portion of an extended object acts like a point source, and an infinite number of rays originate from each of these points. To form the image of a point, rays of light from that point, after refraction from the lens, intersect. Even if half of the lens is covered, light rays from all parts of the object can still pass through the uncovered portion of the lens and converge to form a complete image at the same position. However, the brightness or intensity of the image will be reduced because the number of rays forming the image is reduced by half.

Experiment: One-half of a convex lens covered with black paper is taken. An object is placed infront of it, say beyond 2F₁ It produces a diminished, real and inverted image between F₂ and 2F₂. Experiment is repeated by placing object at different positions. In all cases image is formed.

10. An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.

Answer: Given:
Object height, h = +5 cm
Object distance, u = -25 cm
Focal length of converging (convex) lens, f = +10 cm

We need to find the image distance (v), image height (h’), and nature of the image.
Using the lens formula:

1/v – 1/u = 1/f
⇒ 1/v – 1/(-25 cm) = 1/(10 cm)
⇒ 1/v + 1/25 = 1/10
⇒ 1/v = 1/10 – 1/25
⇒ 1/v = (5 – 2)/50
⇒ 1/v = 3/50
⇒ v = 50/3 cm
⇒ v = +16.67 cm

The image is formed at a distance of 16.67 cm on the other side of the lens.

Magnification,

m = h’/h
⇒ m = v/u
⇒ m = (+16.67 cm) / (-25 cm)
⇒ m = -0.67

Now, for the image size:
h’ = m x h
⇒ h’ = (-2/3) x 5 cm
⇒ h’ = -10/3 cm
⇒ h’ = -3.33 cm

So, the position of the image is 16.67 cm on the other side of the lens.
The size of the image is 3.33 cm.
The nature of the image is real, inverted, and diminished.

11. A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.

Answer: Given,
Focal length of concave lens, f = -15 cm
Image distance, v = -10 cm (A concave lens always forms a virtual image on the same side of the lens as the object)

We need to find the object distance (u).

Using the lens formula:
1/v – 1/u = 1/f
⇒ 1/(-10 cm) – 1/u = 1/(-15 cm)
⇒ -1/10 – 1/u = -1/15
⇒ -1/u = -1/15 + 1/10
⇒ -1/u = (-2 + 3)/30
⇒ -1/u = 1/30
⇒ u = -30 cm

Thus, the object is placed 30 cm from the lens on the same side as the image.

12. An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

Answer: Given:
Object distance, u = -10 cm
Focal length of convex mirror, f = +15 cm

We need to find the image distance (v) and the nature of the image.

Using the mirror formula:
1/v + 1/u = 1/f
⇒ 1/v + 1/(-10 cm) = 1/(15 cm)
⇒ 1/v – 1/10 = 1/15
⇒ 1/v = 1/15 + 1/10
⇒ 1/v = (2 + 3)/30
⇒ 1/v = 5/30 = 1/6
⇒ v = +6 cm

The image is formed at a distance of 6 cm behind the mirror.

Magnification,

m = -v/u
⇒ m = -(+6 cm) / (-10 cm)
⇒ m = 6/10
⇒ m = +0.6

So, the position of the image is 6 cm behind the convex mirror.
The nature of the image is virtual, erect, and diminished.

13. The magnification produced by a plane mirror is +1. What does this mean?

Answer: If the magnification produced by a plane mirror is +1, it means:
The positive sign (+) indicates that the image formed is virtual and erect.
The value ‘1’ indicates that the size of the image is equal to the size of the object (h’ = h).
Therefore, a magnification of +1 for a plane mirror signifies that the image is virtual, erect, and of the same size as the object.

14. An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.

Answer: Given:
Object height, h = +5.0 cm
Object distance, u = -20 cm
Radius of curvature of convex mirror, R = +30 cm
Focal length, f = R/2 = +30 cm / 2 = +15 cm

We need to find the image distance (v), nature of the image, and image height (h’).

Using the mirror formula:
⇒ 1/v + 1/u = 1/f
⇒ 1/v + 1/(-20 cm) = 1/(15 cm)
⇒ 1/v – 1/20 = 1/15
⇒ 1/v = 1/15 + 1/20
⇒ 1/v = (4 + 3)/60
⇒ 1/v = 7/60
⇒ v = +60/7 cm
⇒ v = +8.57 cm

The image is formed at a distance of 60/7 cm (or approximately 8.57 cm) behind the mirror.

Magnification, m = -v/u = h’/h
⇒ m = -(+60/7 cm) / (-20 cm)
⇒ m = (60/7) x (1/20)
⇒ m = 3/7
⇒ m = +0.43

Now, for the image size:
h’ = m x h
⇒ h’ = (3/7) x 5.0 cm
⇒ h’ = 15/7 cm
⇒ h’ = +2.14 cm

So, the position of the image is 60/7 cm (approx. 8.57 cm) behind the mirror.
The nature of the image is virtual, erect, and diminished.
The size of the image is 15/7 cm (approx. 2.14 cm).

15. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.

Answer: Given:
Object height, h = +7.0 cm
Object distance, u = -27 cm
Focal length of concave mirror, f = -18 cm

We need to find the image distance (v) (where the screen should be placed), image height (h’), and nature of the image.

Using the mirror formula:
1/v + 1/u = 1/f
⇒ 1/v + 1/(-27 cm) = 1/(-18 cm)
⇒ 1/v – 1/27 = -1/18
⇒ 1/v = 1/27 – 1/18
⇒ 1/v = (2 – 3)/54
⇒ 1/v = -1/54
⇒ v = -54 cm

A screen should be placed at a distance of 54 cm in front of the mirror to obtain a sharp focused image. The negative sign indicates the image is formed on the same side as the object, which is where real images are formed by a concave mirror.

Magnification, m = -v/u = h’/h
⇒ m = -(-54 cm) / (-27 cm)
⇒ m = 54 / (-27) = -2

Now, for the image size:
h’ = m x h
⇒ h’ = (-2) x 7.0 cm
⇒ h’ = -14.0 cm

So, the screen should be placed 54 cm in front of the mirror.
The size of the image is 14.0 cm.
The nature of the image is real, inverted, and enlarged.

16. Find the focal length of a lens of power – 2.0 D. What type of lens is this?

Answer: Given:
Power of the lens, P = -2.0 D

The relationship between power and focal length (f, in metres) is P = 1/f.
So, f = 1/P
⇒ f = 1 / (-2.0 D)
⇒ f = -0.5 metres
⇒ f = -50 cm

The focal length of the lens is -0.5 m or -50 cm.
Since the power of the lens is negative (and consequently the focal length is negative), the lens is a concave lens.

17. A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?

Answer: Given:
Power of the corrective lens, P = +1.5 D

The focal length (f, in metres) is given by f = 1/P.
f = 1 / (+1.5 D)
⇒ f = 1 / (3/2) m
⇒ f = 2/3 m
⇒ f = +0.67 metres or +66.67 cm

The focal length of the lens is +2/3 m (or approximately +66.67 cm).
Since the power of the lens is positive, the lens is a convex lens. A convex lens is a converging lens.
Therefore, the prescribed lens is converging.

Extras

Additional MCQs (Knowledge Based)

1. What phenomenon describes the tendency of light to bend around very small opaque objects and not travel in a straight line?

A. Reflection
B. Refraction
C. Diffraction
D. Dispersion

Answer: C. Diffraction

2. The laws of reflection state that the angle of incidence is equal to the angle of reflection, and the incident ray, the normal, and the reflected ray all lie in the _____________.

A. same plane
B. different planes
C. perpendicular planes
D. parallel planes

Answer: A. same plane

3. A spherical mirror whose reflecting surface is curved outwards is known as a:

A. Concave mirror
B. Convex mirror
C. Plane mirror
D. Parabolic mirror

Answer: B. Convex mirror

4. For a spherical mirror, the center of the sphere of which the mirror’s reflecting surface is a part, is called the:

A. Pole
B. Principal focus
C. Centre of curvature
D. Aperture

Answer: C. Centre of curvature

5. Consider a concave mirror. If incident rays of light are parallel to the principal axis, after reflection they will:

A. Pass through the pole
B. Pass through the centre of curvature
C. Appear to diverge from the focus
D. Converge at the principal focus

Answer: D. Converge at the principal focus

6. The relationship between the radius of curvature (R) and focal length (f) for a spherical mirror of small aperture is:

A. R = f
B. R = 2f
C. f = 2R
D. R = f/2

Answer: B. R = 2f

7. An object is placed at the centre of curvature (C) of a concave mirror. Which of the following describes the image formed?

Person (Object Position) / Image Property
W (At C) / Virtual, erect, magnified
X (At C) / Real, inverted, same size
Y (At C) / Real, inverted, diminished
Z (At C) / Virtual, inverted, same size

A. W
B. X
C. Y
D. Z

Answer: B. X

8. With reference to image formation by a concave mirror, complete the following analogy: Object at infinity : Image at F :: Object at F : _____________.

A. Image at C
B. Image at infinity
C. Image at P
D. Image behind mirror

Answer: B. Image at infinity

9. Which type of mirror is commonly used by dentists to obtain a magnified view of teeth?

A. Convex mirror
B. Plane mirror
C. Concave mirror
D. Cylindrical mirror

Answer: C. Concave mirror

10. Identify the odd one out concerning the nature of images typically formed by a convex mirror.

A. Virtual
B. Erect
C. Diminished
D. Real

Answer: D. Real

11. Which of the following statements are true for the image formed by a convex mirror?
P. It is always real.
Q. It is always virtual.
R. It is always erect.
S. It can be magnified.

A. P and S
B. Q and R
C. P and R
D. Q and S

Answer: B. Q and R

12. According to the New Cartesian Sign Convention for spherical mirrors, which of the following is NOT true?

A. The object is placed to the left.
B. Distances are measured from the pole.
C. Distances to the right are positive.
D. Heights upwards are negative.

Answer: D. Heights upwards are negative.

13. The mirror formula relating object distance (u), image distance (v), and focal length (f) is:

A. 1/v – 1/u = 1/f
B. 1/u – 1/v = 1/f
C. 1/v + 1/u = 1/f
D. v + u = f

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

14. A positive sign for magnification (m) indicates that the image formed by a spherical mirror is:

A. Real
B. Inverted
C. Virtual
D. Magnified

Answer: C. Virtual

15. The bending of light as it passes obliquely from one transparent medium to another is called:

A. Reflection
B. Diffraction
C. Refraction
D. Interference

Answer: C. Refraction

16. When a ray of light travels from air into a glass slab, it bends _____________.

A. towards the normal
B. away from the normal
C. along the normal
D. it does not bend

Answer: A. towards the normal

17. Snell’s law of refraction states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is:

A. Always one
B. A constant
C. Always less than one
D. Always greater than one

Answer: B. A constant

18. The refractive index of water is approximately 1.33. This means that the speed of light in water is approximately:

A. 1.33 times the speed in air
B. Equal to the speed in air
C. 1/1.33 times the speed in air
D. Unrelated to speed in air

Answer: C. 1/1.33 times the speed in air

19. A lens which is thicker at the center and thinner at the edges is known as a:

A. Concave lens
B. Convex lens
C. Plano-concave lens
D. Plano-convex lens

Answer: B. Convex lens

20. A ray of light passing through the optical centre of a thin lens will:

A. Deviate towards the base
B. Deviate away from the base
C. Emerge without any deviation
D. Undergo dispersion

Answer: C. Emerge without any deviation

21. For a convex lens, if an object is placed at 2F₁, the image formed will be at:
Lens Type / Object Position / Image Position
W (Convex) / At 2F₁ / At F₂
X (Convex) / At 2F₁ / At 2F₂
Y (Convex) / At 2F₁ / Beyond 2F₂
Z (Convex) / At 2F₁ / Between F₂ and 2F₂

A. W
B. X
C. Y
D. Z

Answer: B. X

22. A concave lens always produces an image that is:

A. Real, inverted, magnified
B. Virtual, erect, diminished
C. Real, erect, diminished
D. Virtual, inverted, magnified

Answer: B. Virtual, erect, diminished

23. According to the sign convention for lenses, the focal length of a concave lens is always taken as:

A. Positive
B. Negative
C. Zero
D. Infinite

Answer: B. Negative

24. The lens formula is given by the relation:

A. 1/v + 1/u = 1/f
B. 1/v – 1/u = 1/f
C. 1/u – 1/v = 1/f
D. v – u = f

Answer: B. 1/v – 1/u = 1/f

25. The power of a lens is defined as the reciprocal of its _____________.

A. object distance
B. image distance
C. focal length
D. aperture

Answer: C. focal length

26. The SI unit for the power of a lens is:

A. Meter
B. Watt
C. Dioptre
D. Lumen

Answer: C. Dioptre

27. If a lens has a power of +2.0 D, it is a:

A. Concave lens with f = 0.5 m
B. Convex lens with f = 0.5 m
C. Concave lens with f = 2.0 m
D. Convex lens with f = 2.0 m

Answer: B. Convex lens with f = 0.5 m

28. Which of the following materials cannot be used to make a lens?

A. Water
B. Glass
C. Plastic
D. Clay

Answer: D. Clay

29. If an image formed by a concave mirror is virtual, erect, and larger than the object, the object must be placed:

A. At infinity
B. At the centre of curvature
C. Between the pole and principal focus
D. Beyond the centre of curvature

Answer: C. Between the pole and principal focus

30. To obtain a real image of the same size as the object using a convex lens, the object should be placed:

A. At F₁
B. At 2F₁
C. At infinity
D. Between O and F₁

Answer: B. At 2F₁

31. If you stand far from a mirror and your image appears erect, the mirror is likely to be:

A. Only plane
B. Only concave
C. Only convex
D. Either plane or convex

Answer: D. Either plane or convex

32. The magnification produced by a plane mirror is +1. What does this imply?
P. Image is same size as object.
Q. Image is virtual.
R. Image is erect.
S. Image is real.

A. P, Q, R
B. P, S
C. Q, R
D. P, R, S

Answer: A. P, Q, R

33. The straight-line path of light is usually indicated as a:

A. Wavefront
B. Beam
C. Ray
D. Photon

Answer: C. Ray

34. An image formed by a plane mirror is always:

A. Real and inverted
B. Virtual and erect
C. Real and erect
D. Virtual and inverted

Answer: B. Virtual and erect

35. The distance between the pole and the principal focus of a spherical mirror is called the:

A. Radius of curvature
B. Aperture
C. Focal length
D. Object distance

Answer: C. Focal length

36. A ray passing through the centre of curvature of a concave mirror, after reflection, is:

A. Reflected back along the same path
B. Passes through the focus
C. Becomes parallel to principal axis
D. Passes through the pole

Answer: A. Reflected back along the same path

37. According to the New Cartesian Sign Convention, distances measured perpendicular to and above the principal axis are taken as:

A. Negative
B. Positive
C. Zero
D. Infinite

Answer: B. Positive

38. A negative sign in the value of magnification for a mirror indicates that the image is:

A. Virtual and erect
B. Real and inverted
C. Virtual and inverted
D. Real and erect

Answer: B. Real and inverted

39. The speed of light in vacuum is approximately:

A. 3 x 10⁶ m/s
B. 3 x 10⁸ m/s
C. 3 x 10¹⁰ m/s
D. 3 x 10⁴ m/s

Answer: B. 3 x 10⁸ m/s

40. When light travels from a denser medium to a rarer medium, it bends:

A. Towards the normal
B. Away from the normal
C. Does not bend
D. Parallel to the interface

Answer: B. Away from the normal

41. The central point of a lens is its:

A. Principal focus
B. Centre of curvature
C. Optical centre
D. Pole

Answer: C. Optical centre

42. A lens has two principal foci. For a convex lens, rays parallel to the principal axis converge at F₂. What happens if rays parallel to the principal axis are incident from the other side?

A. They diverge from F₁
B. They converge at F₁
C. They pass undeviated
D. They converge at F₂ again

Answer: B. They converge at F₁

43. Magnification (m) produced by a lens is given by h’/h. It is also related to v and u by the formula:

A. m = -v/u
B. m = v/u
C. m = u/v
D. m = -u/v

Answer: B. m = v/u

44. A lens of power -2.5 D has a focal length of:

A. -0.40 m
B. +0.40 m
C. -2.5 m
D. +2.5 m

Answer: A. -0.40 m

45. If two thin lenses of powers P₁ and P₂ are placed in contact, the net power of the combination is:

A. P₁P₂
B. P₁/P₂
C. P₁ + P₂
D. P₁ – P₂

Answer: C. P₁ + P₂

Additional MCQs (Competency Based)

1. Assertion (A): When light travels from air into a glass slab, its path bends.
Reason (R): The speed of light changes as it enters a different transparent medium.

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R does not explain A.
(c) A is true but R is false.
(d) A is false but R is true.

Answer: (a) Both A and R are true and R is the correct explanation of A.

2. Scenario: A student is trying to form a real, inverted image of the same size as an object using a spherical mirror.
Where should the student place the object relative to the mirror?

(a) Between the pole and the principal focus
(b) At the principal focus
(c) At the centre of curvature
(d) Beyond the centre of curvature

Answer: (c) At the centre of curvature

3. Stimulus: “The refractive index of water is 1.33 and that of crown glass is 1.52.”
Based on this information, which statement is correct regarding the speed of light?

(a) Light travels faster in water than in crown glass.
(b) Light travels faster in crown glass than in water.
(c) Light travels at the same speed in both water and crown glass.
(d) The speed of light cannot be compared using refractive indices.

Answer: (a) Light travels faster in water than in crown glass.

4. Assertion (A): A convex mirror is used as a rear-view mirror in vehicles.
Reason (R): Convex mirrors always form an erect, diminished image and have a wider field of view.

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Answer: (a) Both A and R are true and R is the correct explanation of A.

5. Match the position of the object in front of a concave mirror (Column A) with the nature of the image formed (Column B).

Column A (Object Position)	Column B (Image Nature)
(i) At infinity	1. Real, inverted, enlarged
(ii) Between F and C	2. Virtual, erect, enlarged
(iii) At F	3. Real, inverted, point-sized
(iv) Between P and F	4. Real, inverted, highly enlarged

Codes:
(a) (i)-3, (ii)-1, (iii)-4, (iv)-2
(b) (i)-1, (ii)-3, (iii)-2, (iv)-4
(c) (i)-3, (ii)-4, (iii)-1, (iv)-2
(d) (i)-4, (ii)-2, (iii)-3, (iv)-1

Answer: (a) (i)-3, (ii)-1, (iii)-4, (iv)-2

6. An object is moved from infinity towards the pole of a concave mirror. Arrange the following characteristics of the image in the order they would generally be observed for its size:
(i) Same size as object
(ii) Highly diminished, point-sized
(iii) Enlarged
(iv) Diminished

(a) (ii) → (iv) → (i) → (iii)
(b) (iv) → (ii) → (iii) → (i)
(c) (ii) → (i) → (iv) → (iii)
(d) (iii) → (i) → (iv) → (ii)

Answer: (a) (ii) → (iv) → (i) → (iii)

7. A spherical mirror has a radius of curvature of 30 cm. What is its focal length?

(a) 30 cm
(b) 15 cm
(c) 60 cm
(d) 7.5 cm

Answer: (b) 15 cm

8. Assertion (A): When a ray of light passes from a rarer medium to a denser medium, it bends towards the normal.
Reason (R): The speed of light is higher in a rarer medium than in a denser medium.

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Answer: (a) Both A and R are true and R is the correct explanation of A.

9. Scenario: A dentist uses a mirror to get a magnified view of a patient’s tooth. The image formed is virtual and erect.
What type of mirror is the dentist using, and where is the tooth placed relative to the mirror’s focal point (F) and pole (P)?

(a) Convex mirror, tooth beyond F
(b) Concave mirror, tooth between P and F
(c) Plane mirror, tooth at any distance
(d) Concave mirror, tooth at F

Answer: (b) Concave mirror, tooth between P and F

10. An object of height 4 cm is placed in front of a spherical mirror. The magnification produced is -1.5. What is the height of the image, and what does the negative sign indicate?

(a) Height 6 cm, image is virtual
(b) Height 2.67 cm, image is real
(c) Height 6 cm, image is real and inverted
(d) Height 2.67 cm, image is virtual and erect

Answer: (c) Height 6 cm, image is real and inverted

11. Match the optical phenomenon (Column A) with the primary principle involved (Column B).

Column A	Column B
(i) Twinkling of stars	1. Reflection by a convex surface
(ii) Formation of a rainbow	2. Reflection by a concave surface
(iii) Image in shaving mirror	3. Atmospheric refraction
(iv) Rear-view mirror function	4. Dispersion of light

Codes:
(a) (i)-4, (ii)-3, (iii)-1, (iv)-2
(b) (i)-3, (ii)-4, (iii)-2, (iv)-1
(c) (i)-3, (ii)-1, (iii)-4, (iv)-2
(d) (i)-1, (ii)-2, (iii)-3, (iv)-4

Answer: (b) (i)-3, (ii)-4, (iii)-2, (iv)-1

12. A ray of light is incident on a rectangular glass slab placed in air. Arrange the following events in the correct sequence as the ray passes through and emerges from the slab:

(i) Ray bends away from the normal at the glass-air interface.
(ii) Ray travels in a straight line within the glass slab.
(iii) Ray bends towards the normal at the air-glass interface.
(iv) Emergent ray is parallel to the incident ray.

(a) (iii) → (ii) → (i) → (iv)
(b) (ii) → (iii) → (iv) → (i)
(c) (iii) → (i) → (ii) → (iv)
(d) (i) → (ii) → (iii) → (iv)

Answer: (a) (iii) → (ii) → (i) → (iv)

13. Stimulus: “For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length.”
If a concave mirror has a focal length of 20 cm, what is its radius of curvature?

(a) 10 cm
(b) 20 cm
(c) 40 cm
(d) 5 cm

Answer: (c) 40 cm

14. Assertion (A): The power of a convex lens is positive.
Reason (R): A convex lens converges parallel rays of light to its principal focus, and its focal length is considered positive according to sign conventions.

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Answer: (a) Both A and R are true and R is the correct explanation of A.

15. Scenario: A student places an object 30 cm in front of a convex lens of focal length 15 cm.
What will be the nature and position of the image formed?

(a) Real, inverted, and at 30 cm on the other side.
(b) Virtual, erect, and at 10 cm on the same side.
(c) Real, inverted, and at 15 cm on the other side.
(d) Virtual, erect, and at 30 cm on the other side.

Answer: (a) Real, inverted, and at 30 cm on the other side.

16. A lens has a power of -2.5 D. What is its focal length and what type of lens is it?

(a) Focal length -0.4 m, convex lens
(b) Focal length +0.4 m, concave lens
(c) Focal length -40 cm, concave lens
(d) Focal length +40 cm, convex lens

Answer: (c) Focal length -40 cm, concave lens

17. Match the term related to spherical mirrors/lenses (Column A) with its description (Column B).

Column A	Column B
(i) Pole (P)	1. Point on principal axis where parallel rays converge after reflection
(ii) Optical Centre (O)	2. Effective diameter of the reflecting surface or lens
(iii) Principal Focus (F) of concave mirror	3. Central point of the reflecting surface of a spherical mirror
(iv) Aperture	4. Central point of a lens through which a ray passes undeviated

Codes:
(a) (i)-4, (ii)-3, (iii)-2, (iv)-1
(b) (i)-3, (ii)-1, (iii)-4, (iv)-2
(c) (i)-3, (ii)-4, (iii)-1, (iv)-2
(d) (i)-1, (ii)-2, (iii)-3, (iv)-4

Answer: (c) (i)-3, (ii)-4, (iii)-1, (iv)-2

18. An object is placed in front of a convex lens and moved from a position far beyond 2F₁ towards F₁. Arrange the following image positions in the order they would generally be observed:

(i) At 2F₂
(ii) At F₂
(iii) Beyond 2F₂
(iv) At infinity

(a) (ii) → (i) → (iii) → (iv)
(b) (iv) → (iii) → (i) → (ii)
(c) (ii) → (iii) → (i) → (iv)
(d) (iii) → (i) → (iv) → (ii)

Answer: (a) (ii) → (i) → (iii) → (iv)

19. Assertion (A): A ray of light passing through the optical centre of a thin lens emerges without any deviation.
Reason (R): The optical centre is a point within the lens such that the surfaces of the lens at this point are effectively parallel for a thin lens.

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Answer: (a) Both A and R are true and R is the correct explanation of A.

20. Scenario: An object is placed at 10 cm from a concave mirror which produces a three times magnified real image.
Where is the image located?

(a) -30 cm
(b) +30 cm
(c) -3.33 cm
(d) +3.33 cm

Answer: (a) -30 cm

21. The refractive index of diamond is 2.42. The speed of light in vacuum is 3 x 10⁸ m/s. What is the speed of light in diamond?

(a) 2.42 x 10⁸ m/s
(b) 7.26 x 10⁸ m/s
(c) 1.24 x 10⁸ m/s
(d) 3 x 10⁸ m/s

Answer: (c) 1.24 x 10⁸ m/s

22. Match the type of lens/mirror (Column A) with a common application (Column B).

Column A	Column B
(i) Concave mirror	1. Correcting myopia
(ii) Convex mirror	2. Magnifying glass
(iii) Convex lens	3. Vehicle headlights
(iv) Concave lens	4. Rear-view mirror in vehicles

Codes:
(a) (i)-2, (ii)-1, (iii)-4, (iv)-3
(b) (i)-3, (ii)-4, (iii)-2, (iv)-1
(c) (i)-4, (ii)-3, (iii)-1, (iv)-2
(d) (i)-3, (ii)-1, (iii)-2, (iv)-4

Answer: (b) (i)-3, (ii)-4, (iii)-2, (iv)-1

23. A student performs an experiment with a convex lens to form images of an object placed at different distances. Arrange the following object positions in increasing order of the size of the real image formed:

(i) At 2F₁
(ii) Between F₁ and 2F₁
(iii) Beyond 2F₁

(a) (iii) → (i) → (ii)
(b) (ii) → (i) → (iii)
(c) (i) → (iii) → (ii)
(d) (iii) → (ii) → (i)

Answer: (a) (iii) → (i) → (ii)

24. Assertion (A): When an object is placed between the pole and focus of a concave mirror, the image formed is virtual, erect, and magnified.
Reason (R): The reflected rays appear to diverge from a point behind the mirror.

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Answer: (a) Both A and R are true and R is the correct explanation of A.

25. Scenario: A person is using a lens to read very small print in a book. The lens produces an upright and larger image of the print.

What kind of lens is being used, and where is the print located relative to the lens’s focal point (F) and optical centre (O)?

(a) Concave lens, print between O and F
(b) Convex lens, print between O and F
(c) Concave lens, print at F
(d) Convex lens, print at 2F

Answer: (b) Convex lens, print between O and F

26. An object is placed 20 cm in front of a concave mirror, and a real image is formed at 60 cm from the mirror on the same side. What is the magnification of the image?

(a) -3
(b) +3
(c) -0.33
(d) +0.33

Answer: (a) -3

27. Match the sign convention term (Column A) for spherical mirrors/lenses with its typical sign (Column B), assuming the object is placed to the left.

Column A	Column B
(i) u (object distance)	1. Positive
(ii) f (focal length of convex mirror)	2. Negative
(iii) h’ (height of virtual, erect image)
(iv) P (power of concave lens)

Codes:
(a) (i)-2, (ii)-1, (iii)-1, (iv)-2
(b) (i)-1, (ii)-2, (iii)-2, (iv)-1
(c) (i)-2, (ii)-1, (iii)-2, (iv)-1
(d) (i)-1, (ii)-1, (iii)-1, (iv)-2

Answer: (a) (i)-2, (ii)-1, (iii)-1, (iv)-2

28. Sequence the steps to determine the focal length of a concave mirror using a distant object (like the sun):

(i) Measure the distance between the mirror and the paper.
(ii) Hold a concave mirror facing the distant object.
(iii) Move a sheet of paper in front of the mirror until a sharp, bright spot is formed.
(iv) The measured distance is the approximate focal length.

(a) (ii) → (iii) → (i) → (iv)
(b) (iii) → (ii) → (iv) → (i)
(c) (ii) → (i) → (iii) → (iv)
(d) (i) → (iii) → (ii) → (iv)

Answer: (a) (ii) → (iii) → (i) → (iv)

Additional Questions and Answers

1. What makes things visible to our eyes?

Answer: During the day, sunlight helps us to see objects. An object reflects light that falls on it. This reflected light, when received by our eyes, enables us to see things.

2. What is the path taken by light usually called?

Answer: The straight-line path of light is usually indicated as a ray of light.

3. What is the nature of light explained by quantum theory?

Answer: According to the modern quantum theory of light, light is neither a ‘wave’ nor a ‘particle’ – the new theory reconciles the particle properties of light with the wave nature.

4. What is the reflecting surface of a spherical mirror a part of?

Answer: The reflecting surface of a spherical mirror forms a part of a sphere.

5. What is a concave mirror?

Answer: A spherical mirror, whose reflecting surface is curved inwards, that is, faces towards the centre of the sphere, is called a concave mirror.

6. What is a convex mirror?

Answer: A spherical mirror whose reflecting surface is curved outwards, is called a convex mirror.

7. What is the pole of a spherical mirror?

Answer: The centre of the reflecting surface of a spherical mirror is a point called the pole. It lies on the surface of the mirror and is usually represented by the letter P.

8. What is the centre of curvature of a concave mirror?

Answer: The sphere of which the reflecting surface of a spherical mirror forms a part has a centre. This point is called the centre of curvature of the spherical mirror. It is represented by the letter C. The centre of curvature is not a part of the mirror; it lies outside its reflecting surface. The centre of curvature of a concave mirror lies in front of it.

9. What is the principal axis?

Answer: A straight line passing through the pole and the centre of curvature of a spherical mirror is called the principal axis. The principal axis is normal to the mirror at its pole.

10. What is the principal focus of a concave mirror?

Answer: When a number of rays parallel to the principal axis fall on a concave mirror, the reflected rays all meet or intersect at a point on the principal axis of the mirror. This point is called the principal focus of the concave mirror.

11. What is the focal length of a spherical mirror?

Answer: The distance between the pole and the principal focus of a spherical mirror is called the focal length. It is represented by the letter f.

12. Write the relation between focal length and radius of curvature.

Answer: For spherical mirrors of small apertures, the radius of curvature R is found to be equal to twice the focal length f. This is expressed as R = 2f.

13. What is the nature of the image formed when the object is at the focus of a concave mirror?

Answer: When the object is at the focus F of a concave mirror, the image formed is real and inverted.

14. What is the nature of the image formed by a convex mirror when the object is at infinity?

Answer: When the object is at infinity, the image formed by a convex mirror is virtual and erect.

15. What kind of image is always formed by a convex mirror?

Answer: Convex mirrors always give an erect, though diminished, image.

16. Name a device that uses a concave mirror to produce heat.

Answer: Solar furnaces use large concave mirrors to concentrate sunlight to produce heat.

17. Why are convex mirrors used in vehicles?

Answer: Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles because they enable the driver to see traffic behind him/her to facilitate safe driving. Convex mirrors are preferred because they always give an erect, though diminished, image. Also, they have a wider field of view as they are curved outwards, thus enabling the driver to view a much larger area than would be possible with a plane mirror.

18. What is the New Cartesian Sign Convention in spherical mirrors?

Answer: In the New Cartesian Sign Convention for reflection by spherical mirrors, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (XX’) of the coordinate system. The conventions are as follows:

(i) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
(ii) All distances parallel to the principal axis are measured from the pole of the mirror.
(iii) All the distances measured to the right of the origin (along +x-axis) are taken as positive while those measured to the left of the origin (along –x-axis) are taken as negative.
(iv) Distances measured perpendicular to and above the principal axis (along +y-axis) are taken as positive.
(v) Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative.

19. Write the mirror formula.

Answer: The mirror formula, which gives the relationship between the object distance (u), the image distance (v), and the focal length (f), is expressed as:
1/v + 1/u = 1/f

20. What is magnification in spherical mirrors?

Answer: Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. It is expressed as the ratio of the height of the image (h’) to the height of the object (h). It is usually represented by the letter m.
So, m = Height of the image (h’) / Height of the object (h)
or, m = h’/h.
The magnification m is also related to the object distance (u) and image distance (v). It can be expressed as:
Magnification (m) = h’/h = -v/u.

21. What does a positive magnification indicate?

Answer: A positive sign in the value of the magnification indicates that the image is virtual.

22. What is refraction of light?

Answer: When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.

23. State Snell’s law of refraction.

Answer: The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media. This law is also known as Snell’s law of refraction. This is true for angle 0 < i < 90°. If i is the angle of incidence and r is the angle of refraction, then, sin i / sin r = constant.

24. What is the refractive index of a medium?

Answer: The constant value from Snell’s law, which is the ratio of sine of angle of incidence to the sine of angle of refraction, is called the refractive index of the second medium with respect to the first. The absolute refractive index of a medium is simply called its refractive index.

25. What is the speed of light in vacuum?

Answer: Light travels fastest in vacuum with a speed of 3×10⁸ m s⁻¹.

26. Write the formula for the absolute refractive index.

Answer: If c is the speed of light in air and v is the speed of light in the medium, then, the refractive index of the medium n<sub>m</sub> is given by:
n<sub>m</sub> = Speed of light in air / Speed of light in the medium = c/v.

27. What does it mean if a medium has a higher refractive index?

Answer: In comparing two media, the one with the larger refractive index is an optically denser medium than the other.

28. What are optically denser and rarer media?

Answer: The terms ‘rarer medium’ and ‘denser medium’ actually mean ‘optically rarer medium’ and ‘optically denser medium’, respectively. In comparing two media, the one with the larger refractive index is an optically denser medium than the other. The other medium of lower refractive index is optically rarer.

29. What happens to the speed of light when it moves from a rarer to a denser medium?

Answer: A ray of light travelling from a rarer medium to a denser medium slows down and bends towards the normal.

30. What is a convex lens also called?

Answer: A convex lens converges light rays, hence convex lenses are also called converging lenses.

31. What is a concave lens also called?

Answer: A double concave lens diverges light rays. Such lenses are also called diverging lenses.

32. What is the optical centre of a lens?

Answer: The central point of a lens is its optical centre. It is usually represented by the letter O.

33. What is the principal axis of a lens?

Answer: An imaginary straight line passing through the two centres of curvature of a lens is called its principal axis.

34. What is the principal focus of a convex lens?

Answer: When several rays of light parallel to the principal axis are falling on a convex lens, these rays, after refraction from the lens, converge to a point on the principal axis. This point on the principal axis is called the principal focus of the lens.

35. Write the lens formula.

Answer: The lens formula is expressed as:
1/v – 1/u = 1/f

36. What is magnification in lenses?

Answer: The magnification produced by a lens is defined as the ratio of the height of the image and the height of the object. If h is the height of the object and h’ is the height of the image given by a lens, then the magnification m produced by the lens is given by:
m = Height of the Image (h’) / Height of the object (h)

37. What is the sign of focal length of a concave lens?

Answer: According to the convention, the focal length of a concave lens is negative.

38. What is the unit of power of a lens?

Answer: The SI unit of power of a lens is ‘dioptre’.

39. Define 1 dioptre of power.

Answer: 1 dioptre is the power of a lens whose focal length is 1 metre.

Ron'e Dutta

Ron'e Dutta is a journalist, teacher, aspiring novelist, and blogger who manages Online Free Notes. An avid reader of Victorian literature, his favourite book is Wuthering Heights by Emily Brontë. He dreams of travelling the world. You can connect with him on social media. He does personal writing on ronism.

Get notes of other classes and subjects

NBSE	SEBA/AHSEC
NCERT	TBSE
WBBSE/WHCHSE	ICSE/ISC
BSEM/COHSEM	Custom Notes for Teachers
MBOSE	Question Papers

Notify change in syllabus/books	Sell PDFs of your books
Request notes not available now	Share PDFs of question papers