Question

A screen is placed 90 cm from an object . The image of the object on the screen is formed by convex lens at two different locations separated by 20 cm . Determine the focal length of the lens (b) suppose the object has a size of 10 cm, and in one case the image is half of its size. Determine image size when lens is displaced to second position

Answer 1

When the object and screen (where image forms) are D = 90cm apart, a

displacement of lens (x=20cm) produces image on screen.

By lens. Displacement method focal length :-

$f=\frac{D^2-x^2}{4D}=\frac{{90}^2-{20}^2}{2\times 90}\simeq 42.78cm.$

Now, height of object, h= 10cm. In one case, Image size is by = 5cm.

In other case the image size is $h_2$, which is related by :-

$h=\sqrt{h_1{h}_2}$

$\Rightarrow h_1=\frac{h^2}{h_1}=\frac{{10}^2}{5}=20cm$ (Ans)