Question

The distance of an object from the focus of a convex mirror of radius of curvature ${}^{\prime }{b}^{\prime }$ is ${}^{\prime }{a}^{\prime }$. Then the distance of the image from the focus is?

• A. $\frac{ab}{2a+b}$
• B. $\frac{a}{b^2}$
• C. $\frac{a^2}{4b}$
• D. $\frac{b^2}{4a}$

Answer 1

The correct option is D $\frac{b^2}{4a}$

Focal length $=\frac{b}{2}$

lens formula

$\begin{array}{c}\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\ \frac{1}{b_2}=\frac{1}{v}+\frac{1}{-(a-b_2)}\\ \frac{2}{b}+\frac{2}{2a-b}=\frac{1}{v}\\ v=\frac{b(2a-b)}{4a}\end{array}$

Distance of image from focus

$\begin{array}{c}=\frac{b}{2}-\frac{b(2a-b)}{4a}\\ =\frac{b}{4}[2-\frac{2a-b}{a}]\\ =\frac{b^2}{4a}\end{array}$

So $D$ is correct.