Question

Focal length of the plano-convex lens is $15cm$. A small object is placed at $A$ as shown in the figure. The plane surface is silvered. The image will form at

• A. $60cm$ to the left of lens
• B. $12cm$ to the left of lens
• C. $60cm$ to the right of lens
• D. $30cm$ to the left of lens

Answer 1

The correct option is B $12cm$ to the left of lens

A ray from point O at first gets refracted from the curved surface of focal length, $f_l=15cm$ and then reflects from the plane mirror. Hence the plano- convex lens will become a curved mirror of focal length $F$.

$\frac{1}{F}=\frac{1}{f_m}-\frac{2}{f_l}$ where $f_m$ is focal length of mirror used.

$\frac{1}{F}=\frac{1}{\infty }-\frac{2}{15}$

$F=\frac{-15}{2}cm$

Using mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{F}$

For $u=-20$, $\frac{1}{v}+\frac{1}{-20}=\frac{-2}{15}$

Thus $v=-12cm$

Thus the final image will form at 12 cm to the left of lens.