Question

1) One student uses a lens of focal length 50 cm and another of -50 cm. What is the focal
length, nature of the lens and its power used by each of them?​

Answer 1

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Answer 2

Given:

A lens has a focal length of 50 cm and another of -50 cm.

To Find:

We have to find the focal  length, nature of the lens, and its power used by each of them

Solution:

For finding the Nature of the lens:-

For a convex lens, the focal length is always positive i.e.  $f>0$                     and for a concave lens, the focal length is always negative i.e. $f<0$

$\therefore$ The nature of the lens with  $f=50 cm$ is convex and the nature of the lens with $f=-50cm$ is concave.

Now, for finding the power :-

We know that, the power of a lens in Dioptre ($D$) is equal to the reciprocal of focal length taken in meters.

We also know that $1m=100cm$.

$\therefore$ For convex lens the focal length in meters is  $f=\frac{50}{100} =0.5m$

and for the concave lens, it is  $f=\frac{-50}{100} =-0.5m$

$\therefore$ Power for the convex lens is

$P = \frac{1}{0.5} = 2D$

and power for the concave lens is

$P=\frac{1}{-0.5} =-2D$

Hence, we get,

For a lens with a focal length $50cm$ :-

• Nature of the lens = Convex
• Power of the lens = $2D$

For a lens with a focal length $-50cm$ :-

• Nature of lens = Concave
• Power of the lens = $-2D$