Light - Reflection and Refraction

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

a) Water

b) Plastic

c) Glass

d) Clay

Solution:

Lenses can be made from transparent material. Clay is an opaque material,

whereas water and glass are transparent materials. One may think of how plastic

can be used to make a lens. Certain types of plastic can be transparent, and

hence, we can create a lens out of them. One may wonder how water can be

used to make a lens. Did you ever see a fish bowl, which is almost spherical in

shape? When you look through the bowl filled with water, you observe that

distant objects on the other side of the bowl appeared inverted. Thus , the water

in the bowl acts like a convex lens.

Correct Answer: D

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 principle 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 principle focus.

Solution:

When an object is placed between the pole and the principle focus of a concave

mirror, the image of the object is virtual, erect and magnified.

Correct Answer: D

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Where an object should be placed in front of a convex lens to get real image of

the size of the object?

a) At the principle focus of the lens

b) At twice the focal length

c) At infinity

d) Between the optical centre of the lens and its principle focus.

Solution:

When an object is placed at a distance that is double the focal length, of the

given convex lens, the image of the object is real, inverted and of the same size

as that of the object.

Correct Answer: B

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.

Solution:

The focal length of a convex mirror and that of a convex lens are considered

positive, according to the sign convention. On the other hand, the focal length of

a concave mirror and concave lens is considered to be negative, according to the

same convention.

Correct Answer: A

No matter how far you stand from a mirror, your image appears erect. The

mirror is likely to be

a) Plane

b) Concave

c) Convex

d) Either plane or convex

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Solution:

In a plane and a convex mirror, the image formed are always erect. The

difference lies in the magnification. In a plane mirror, the magnification is

always equal to one, while in a convex mirror, the magnification is always less

than one.

Correct Answer: D

Which of the following lenses would you prefer to use while reading small

letters found in a dictionary?

Solution:

A convex lens of short focal length serves as a magnifying glass, and hence, is

used in reading the small print in books.

Correct Answer: D

We wish to obtain an erect image of an object, using a concave mirror of focal

length 15cm. 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.

Solution

Given, focal length = 15cm

Therefore Range of the object from the mirror will be 0 to 15 cm (excluding 15)

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Nature of image is Virtual and size of the image is Greater than the object.

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

Solution:

a) Concave mirrors, because the bulb is placed at the focus and the light is

reflection from the mirror as a parallel beam.

b) Convex mirror, because it helps form images of object in a larger field of

view.

c) Concave mirror, because it helps in focussing a parallel solar beam to its

principal focus.

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 observation

Solution:

Even though one – half of a convex lens is covered with a black paper. The lens

produces a complete image of the object as all the right rays reflected from the

object can pass through the upper portion of the lens, and hence a full image of

light passing through the lens is restricted.

An object 5cm in length is held 25cm away from a converging lens of focal

length 10cm. Draw the ray diagram and find the position, size an the nature of

the image formed.

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Solution

Diagram

Given, size of object = 5 cm

Object distance, u = - 25 cm

Focal Length, f = 10 cm

The lens formula is �� =

�� -

��

��� =

�� - �

���

⇒ �� =

��� -

�� =

������� =

���

= �

⇒ v = � = 16.67 cm

Therefore Image distance (v) = 16.67 cm

Image will be real and inverted.

Magnification, m = ������������������� =

���������������������������

��������� =

��/ ��

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⇒ Image size = �

×� × 5 = ��

= 3.33 cm

A concave lens of the focal length 15cm forms an image 10cm from the lens.

How far is the object placed from the lens? Draw the ray diagram.

Solution:

Given,

Focal length of the concave lens is 15cm

Distance of the image from the lens is 10 cm

Hence, the focal length of concave lens is – 15cm

Image distance from the lens (v) = -10 cm

The lens formula is � =

�� -

�� where

f = Focal length

v = image distance

u = Object distance

��� =

���� -

��

�� = − ��� +

��

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�� =

��#���� =

�� =

�� �

⇒ u = - 30 cm

Thus, object distance = 30cm

An object is placed of 10 cm from a convex mirror of focal length 15cm. Find

the position and nature of the image.

Solution:

Object distance u = - 10 cm

Focal length, f = 15cm

The mirror formula is �� =

�� +

��

Where = focal length

f = Focal length

v = image distance

u = Object distance

�� =

�� + � �

���

⇒ �� =

�� +

��� =

��#��� =

��� =

�$

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⇒ �� =

�$

⇒ v = 6 cm

Image is formed behind the mirror 6cm away from its pole.

Nature of the image is virtual, Erect and Diminished.

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

Solution:

The size of the image produced by a plane mirror is equal to the size of the

object.

An object 5.0cm in length is placed at a distance of 20cm in front of a convex

mirror of radius curvature 30cm. Find the position of the image, its nature and

size.

Solution

Given

Length of the object = 5 cm

Distance of object from the mirror = 20 cm

Therefore object distance u = - 20cm

Radius of curvature R, = 30 cm

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Focal length (F) of a mirror = %�

⇒ f = �� = 15 cm

The mirror formula is �� =

�� +

�� Where

f = Focal length

v = image distance

u = Object distance

�� =

�� + � �

��� �� =

�� +

��� = =

��#���� =

�� =

&$�

⇒ �� =

$�& = 8.57 cm

Image distance = 8.57 cm

Image formed is VIRTUAL, ERECT and DIMINISHED.

Magnification m = ������������������� =

���������������������������

��������� =

�$�/&���

⇒ Image size = $�

&×�� × 5

= �& = 2.14 cm

An object of size7.0cm is placed at 27cm in front of a concave mirror of focal

length 18cm. At what distance from the mirror should a screen be placed, so

that a sharp focussed image can be obtained? Find the size and nature of the

image.

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Solution:

Given, size of the object = 7 cm

Focal Length f = 18 cm

Object distance u = 27 cm

Image will be real, inverted and magnified

The mirror formula is �� =

�� +

�� Where

���' =

�� + � �

��& �� =

��& -

��' = =

�'#�&�&�' =

�� =

�(�&�'

⇒ �� =

��)

= v = - 54cm

Screen has to be placed 54 cm from the mirror for a sharp and focused image.

Magnification

Magnification m = ������������������� =

���������������������������

���������& =

)�&

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⇒ Image size = )�& × 7 = 14 cm

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

Solution:

Given, power of the lens = -2.0 D

⇒ given lens is concave ( because power of concave lens is negative)

Power f a lens, P = �

������*�� where

f is the focal length of lens expressed in metres.

-2.o = �

������*��

⇒ f ( in metres) = �

��.� = - 50 cm

Therefore Focal length of the given lens is 50 cm and the given is a a negative

lens i.e. a Concave Lens

A doctor has prescribed a corrective lens of power +1.5D. Find the focal length

of the lens. Is the prescribed lens diverging or converging?

Solution:

Given, power of the lens is + 1.5D

⇒ Given lens is convex (power of convex lens is positive)

Power of a lens, P = �

������*�� where f is the focal length of lens expressed in

metres.

1.5 = �

������*��

⇒ f ( in metres) = ��. = 0.67 cm

Therefore Focal length of the lens is 0.67 cm and it is a convex Lens.

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