Question

An object is placed 20 cm in front of a convex lens. The image is formed on a screen at a distance of 12 cm from the lens. The Power of the lens is 

A. +3.33 D

B. - 3.33 D

C. + 13.33 D

D. - 13.33 D​

Answer 1

Answer :-

Power of the lens is + 13.33 D [Option.C] .

Explanation :-

We have :-

→ Distance of the object = 20 cm

→ Distance of the image = 12 cm

______________________________

According to sign convention :-

• u = -20 cm

• v = + 12 cm

Now, let's calculate the focal length of the mirror by using the lens formula .

1/v - 1/u = 1/f

⇒ 1/12 - 1/(-20) = 1/f

⇒ 1/12 - (-1)/20 = 1/f

⇒ (5 + 3)/60 = 1/f

⇒ 8/60 = 1/f

⇒ 8f = 60

⇒ f = 60/8

⇒ f = 7.5 cm

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When focal length is in cm , then the relationship bewteen power and focal length of a lens is given by :-

P = 100/f

⇒ P = 100/7.5

⇒ P = + 13.33 D

Answer 2

Given :-

An object is placed 20 cm in front of a convex lens. The image is formed on a screen at a distance of 12 cm from the lens.

To Find :-

Power

Solution :-

We know that

1/v - 1/u = 1/f

Where

u = Object distance

v = Image distance

f = focal length

1/12 - 1/-20 = 1/f

1/12 + 1/60 = 1/f

5 + 3/60 = 1/f

8/60 = 1/f

2/15 = 1/f

15 = 2f

f = 15/2

Now,

P = 1/f

Where

P = power

f = focal length

P = 100/(15/2)

P = 100/1 × 2/15

P = 200/15

P = 40/3

P = 13.33 D or + 13.33 D

∴ Option C is correct