Question

A lens forms a real image of an object on a
screen placed at a distance of 100 cm from the
object. If the lens is moved by 20 cm towards the
screen, another image of the object is formed on
the screen. Then the focal length of the lens is??​

Answer 1

As we fix the object and screen only move the lens to form images, we can see that object to lens distance u and image to lens distance are interchanged. In a former case object is placed beyond 2F to get diminished image. In later case object is placed between F and 2F and we get a magnified image.

From figure it can be seen that u+v = 100; and u-v = 20;

By solving we get u =60 cm and v = 40 cm.

 

hence focal length f is given by:

using lens formula, wid v= 40 , u = -60

u will get f = 24 cm

Answer 2

The value of focal length is 24 cm.

Explanation:

We are given that:

Distance of image = 100 cm

Distance covered by lens = 20 cm

The focal length of the lens = ?

Now using lens mirror formula:

1 / v - 1/ u = 1 / f

1 / 100 - u + 1 / u = 1 / f     ----(1)

1 / 80 - u + 1 / u + 20 = 1/ f      ----(2)

From equation (1) and (2) we can say that.

1 / 100 - u + 1/ u = 1 / 80 - u + 1 / u + 20

20 / [u] [u + 20 ] = 1 / [80 - u] [ 100 - u ]

u^2 + 20 u = u^2 - 180 u + 8000

u = 40

Now put the value in the formula.

1/ 60 + 1 / 40 = 1 / f

Focal length = 24 cm

Thus the value of focal length is 24 cm.