Question

Radius of curvature of convex mirror is $40cm$ and the size of the object is twice as that of the image. Then image distance is (in cm).

• A. $10$
• B. $20$
• C. $40$
• D. $30$

Answer 1

The correct option is A $10$

Given

$\begin{array}{c}R=40cm,f=\frac{R}{2}=20cm\\ \frac{h_i}{h_0}=\frac{-v}{u}\\ \frac{h_i}{2h_i}=\frac{-v}{\left(-u\right)}\\ \frac{v}{u}=\frac{1}{2}\\ u=2v\end{array}$

For convex mirror

$\begin{array}{c}\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\\ \frac{1}{20}=\frac{1}{v}-\frac{1}{2v}\\ \frac{1}{20}=\frac{1}{2}\times \frac{1}{v}\\ v=\frac{20}{2}=10cm\end{array}$