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)

$21.4 \,cm$

Answer 2

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