Question

A convex lens of focal length $40cm$ is held co-axially $12cm$ above a convex mirror of focal length $18cm$, fig. A luminous point object placed $dcm$ above the lens on its axis gives rise to an image coincident with itself. The value of $d$ would be

• A. $30cm$
• B. $24cm$
• C. $45cm$
• D. $15cm$

Answer 1

The correct option is D $15cm$

$\begin{array}{c}\text{The lens forms the image on}\\ \text{the centre of curvature of}\\ \text{mirror, so that the rays}\\ \text{will retrace their path}\\ \text{i.e.}V=-24\text{(for lens)}\end{array}$

$\begin{array}{cc}\text{for lens}& \frac{1}{v}-\frac{1}{4}=\frac{1}{f}\\ \therefore & >\frac{1}{-24}-\frac{1}{(-d)}=\frac{1}{40}\\ & \Rightarrow \frac{1}{d}=\frac{1}{40}+\frac{1}{24}\\ & \Rightarrow \frac{1}{d}=\frac{3+5}{120}\\ & \Rightarrow d=\frac{120}{8}\\ & \Rightarrow d=15cm\\ \text{Hence,}& \text{(D) is correct option.}\end{array}$