Question

A small piece of wire bent into an L shape, with upright and horizontal portions of equal lengths, is placed with the horizontal portion along the axis of the concave mirror whose radius of curvature is $10 \,cm$. If the bend is $20\, cm$ from the pole of the mirror, then the ratio of the lengths of the images of the upright and horizontal portions of the wire is

• A. $1: 2$
• B. $3: 1$
• C. $1: 3$
• D. $2: 1$

Answer 1

Answer: (B)

For upright portion,
$m=\frac{f}{f-u}=\frac{\frac{-10}{2}}{\frac{-10}{2}-(-20)}$
$=\frac{-5}{-5+20}=\frac{-5}{15}=-\frac{1}{3}$
For horizontal portion, magnification is $\left(-\frac{1}{3}\right)^{2}$ i.e., $\frac{1}{9}$
Required ratio is $\frac{-1 / 3}{1 / 9}=-3: 1$