Question

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

• A. $42.8cm$
• B. $21.4cm$
• C. $10.7cm$
• D. $5.5cm$

Answer 1

Answer: (B)

The image of the object can be located on the screen for two positions of convex lens such that $u$ and $v$ are exchanged.
The separation between two positions of the lens is
$d=20cm$

From the figure.
$u_i+v_i=90cm$
$v_i-u_i=20cm$
Solving
$v_1=55cm,u_1=35cm$
From lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{55}-\frac{1}{-35}=\frac{1}{f}$ or
$\frac{1}{55}+\frac{1}{35}=\frac{1}{f}$
$\Rightarrow f=\frac{55\times 35}{90}$
$=21.4cm$