Question

A thin rod of length $\frac{f}{3}$ lies along the axis of a concave mirror of focal length $f$. One end of its image touches at end of the rod. The length of the image is :

• A. $f$
• B. $\frac{1}{2}f$
• C. $2f$
• D. $\frac{1}{4}f$

Answer 1

The correct option is B $\frac{1}{2}f$

Since one end of rod touches image that end is at center of curvature.

From lens formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{3}{5f}=\frac{-1}{f}$

$\frac{1}{v}=\frac{-5}{5f}+\frac{3}{5f}$

$\frac{1}{v}=\frac{-2}{5f}$

$v=-\frac{5f}{2}$

Length of image, $l_{img}=\frac{5f}{2}-\frac{4f}{2}$

$=\frac{f}{2}$