Question

A screen is placed 90 cm away from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Find the focal length of lens.

Answer 1

The image of the object can be located on the screen for two-position of convex lens such that u and v are exchanged.

The separation between two positions of the lens is, d= 20 cm

From the figure,

$u_1+v_1=90cm$

$v_1-u_1=20cm$

Solving,

$v_1=55cm,u_1=35cm$

From lens formula,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{55}-\frac{1}{-35}=\frac{1}{f}$

$\Rightarrow \frac{1}{f}=\frac{1}{55}+\frac{1}{35}=\frac{55\times 35}{90}$
$\Rightarrow f=21.4cm$

Hence, the correct option is $\left(B\right)$