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

Explanation:

CONCEPT:

The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.

The lens whose refracting surface is upside is called a convex lens.

The convex lens is also called a converging lens.

Lens formula is given by:

Where u is object distance, v is image distance and f is the focal length of the lens

CALCULATION:

Given that:

Object distance (u) = - 20 cm

Focal length (f) = 7.5 cm

Use the lens formula:

So image distance (v) = 150/12.5 = 12 cm

Hence option 3 is correct.

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Answer 2

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 .

$\longrightarrow$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