### Page No. – 168

1. Define the principal focus of a concave mirror.
Ans – The principal focus of a concave mirror is a point located on the principal axis of the mirror, where all light rays that are parallel to the principal axis converge after being reflected by the mirror. It is a point of convergence for light, and it is an important characteristic of concave mirrors.

2. The radius of curvature of a spherical mirror is 20 cm. What is its focal length?
Ans –
The radius of curvature (R) of a spherical mirror is 20 cm and its focal length (f) can be calculated using the formula:
1/f = 2/R
R = 20 cm
R = 2f
f = R/2
f = 20 / 2
f = 10 cm.

3. Name a mirror that can give an erect and enlarged image of an object.
Ans –
Concave Mirror

• Position – behind the mirror
• Nature – Real & Inverted
• Size – Enlarged

4. Why do we prefer a convex mirror as a rear-view mirror in vehicles?
Ans –
Convex mirrors are preferred as rear-view mirrors in vehicles because they form virtual, erect & diminished images of the object. A convex mirror gives a wider field of view which makes it easier to see what is happening behind the vehicle.

OR

Convex mirrors are preferred as rear-view mirrors in vehicles because they have certain properties that make them well-suited for this purpose. Some of the reasons why convex mirrors are used in vehicles include:

Wide Field of View: Convex mirrors have a wider field of view than flat mirrors, which makes it easier to see what is happening behind the vehicle. This is important when changing lanes, reversing, or checking for vehicles in the blind spot.

No Distortion: Convex mirrors produce an undistorted image of the objects behind the vehicle. This is because the light from objects at the edge of the mirror is reflected in the center of the mirror, creating an image that is similar in size to the object itself.

Smaller Size: Convex mirrors are smaller than flat mirrors, making them easier to mount on vehicles and giving them a more compact and stylish appearance.

Improved Safety: Convex mirrors provide drivers with a better view of what is happening behind the vehicle, which can improve safety on the road. By allowing drivers to see more of the road behind them, convex mirrors help to reduce the risk of accidents caused by changing lanes, reversing, or merging.

### Page No. – 171

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

Ans – R = +32 cm
f = R/2
f = 32/2
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?
Ans –
u = -10 cm
m = 3
m = h’/h
m = -3
m = -v/u
-3 = -v /-10
v = -30 cm

### Page No. – 176

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?
Ans –
Light always bends towards the normal when entering a denser medium, because the velocity of light decreases in a denser medium, and the path of the light ray changes accordingly.

2. Light enters from air to glass having a refractive index of 1.50. What is the speed of light in the glass? The speed of light in a vacuum is 3x108 m s–1.
Ans –
n = 1.50
Speed of light in glass = ?
Speed of light in Vaccum = 3x108 m/s
n = c/v
1.50 = 3x108 / v
v = 3x108 / 1.5
v = 2x108 m/s

3. Find out, from Table 10.3, the medium having the highest optical density. Also, find the medium with the lowest optical density.
Ans –
Diamond – 2.42
Air – 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 10.3.
Ans –
Kerosene – 1.44
Water – 1.33
Turpentine – 1.47
n ∝ 1/v           (v – speed of light in any medium)
The speed of light in water is the fastest.

5. The refractive index of diamond is 2.42. What is the meaning of this statement?
Ans –
n = 1/v                            [ n ∝ optical density (denser) ]
(i) Diamond – Denser
(ii) n = 2.42 (diamond)
n = c/v
n = speed of light in air/speed of light in a diamond
2.42 = c/speed of light in a diamond
speed of light in diamond = c x 1 / 2.42
speed of light in diamond is reduced to 1/2.42 times in speed of light in air.

### Page No. – 184

1. Define 1 dioptre of power of a lens.
Ans –
P = 1/f
f = 1m
P = 1/1
One dioptre is the power of a lens whose focal length is 1 m.

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.
Ans –
Image – Real & inverted
height of image = height of object [h’=h]
v = +50 cm
m = h’/h = v/u
m = -1/1 = -1 = 50/u
u = -50 cm
f = ?
1/v – 1/u =1/f
1/50 – 1/-50 = 1/f
1/50 + 1/50 = 1/f
1+1/50 = 1/f
1/f = 1/25
f = 25 cm
Power = 1/f
P = 100 / f(cm)
P = 100 /25
Power of lens = +4D.

3. Find the power of a concave lens of focal length 2 m.
Ans – f = -2 m
P = 1/f
P = 1/-2
P = -0.5 D

### Exercise Questions

1. Which one of the following materials cannot be used to make a lens?
(a) Water (b) Glass (c) Plastic (d) Clay
Ans –
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.

Ans – (d) Between the pole of the mirror and its principal focus.
Concave mirror

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.
Ans –
(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.
Ans –
(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.
Ans –
(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.
Ans –
(c) A convex lens of focal length 5 cm.
Convex lens – When an object is at O & F1, the Image is on the same side, virtual, erect & enlarged.
A convex lens is used for magnifying letters.
magnification ∝ 1/ focal length

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.
Ans –
Image – Erect
concave mirror – object between F & P
f = -15 cm
(i) Object distance must be less than 15 cm.
(ii) Image is virtual.
(iii) Image is larger than the object.

8. . Name the type of mirror used in the following situations.
(b) Side/rear-view mirror of a vehicle.
(c) Solar furnace.
Ans – (a) (a) Headlights of a car –
Concave mirror is used because when the light source is placed at the principal focus it produces a powerful parallel beam of light.

(b) Side/rear-view mirror of a vehicle – Convex mirror is used because an Erect, virtual & diminished image is formed.
(c) Solar furnace – Concave mirror is used in solar furnaces. Also known as a converging mirror. It converges the light ray to focus.

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.
Ans-
Yes, the lens produces a complete image but the brightness of the image is low due to no. of rays passing through it.

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.
Ans –
Given – a converging lens, it means it is a Convex lens.
u = -25 cm
f = +10 cm
v = +5 cm   (height of object)
using lens formula –
1/v – 1/u = 1/f
1/v – 1/(-25) = 1/10
1/v = 1/10 – 1/25
1/v = 5 – 2 / 50
v = 50 / 3
v = 16.67 cm (position of image)
m = hi / ho = v / u
m = hi / 5 = 50 /3 / -25
hi / 5 = 50 / 3 x -25
hi = – 5 x 2 / 3
hi = – 3.33 cm
Nature – Real, inverted & smaller than the size of the object.

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.
Ans –
u =?
f = -15 cm
v = – 10cm
Using lens Formula –

u = -30 cm.

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.
Ans –
F = 15 cm
u = -10 cm

v = 6 cm.

Nature – Virtual, Erect & smaller than the size of the object.

13. The magnification produced by a plane mirror is +1. What does this mean?
Ans –
m = hi/ho = +1
hi=ho
m = +1

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.
Ans-
R =+30 cm
we know that
f =R/2
f = 30/2
f = 15 cm.
u = -20 cm
ho = 5 cm
using mirror formula –

v = 8.5 cm.

Nature – Virtual, Erect & smaller than the size of the object.

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.
Ans- f = -18
ho = +7 cm
u = -27 cm
using mirror formula –

v = -54 cm.

m = hi = -7 x 2
hi = -14 cm

Nature – Real, Inverted & larger than the size of the object.

16. Find the focal length of a lens of power – 2.0 D. What type of lens is this?
Ans – P = -2D
P = 1/ f (in m)
f = 1/ P
f = -1/2
f = -0.5 m.
or f = -50 cm.

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?
Ans – P = 1.5 D
P = 1/ f (in m)
f = 1/ P
f = 1/1.5
f = 0.667 m
or f = 66.7 cm

Categories: Class 10 (Science)

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