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.

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

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
$d = 20\,cm$

From the figure.
$u_i + v_i = 90\, cm$
$v_i - u_i = 20 \,cm$
Solving
$v_1 = 55 \,cm, u_1 = 35\, cm$
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} $
$= 21.4\,cm$