Question

Behind a thin converging lens having both the surfaces of the same radius $1cm$, a plane mirror has been placed. The image of an object at a distance of $40cm$ from the lens is formed at the same position. What is the refractive index of the lens?

• A. $1.5$
• B. $5/3$
• C. $9/8$
• D. None of these

Answer 1

The correct option is C $9/8$

${}^{\prime \prime }{O}^{\prime \prime }$ act as the focal point.
Also, $\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$
$\Rightarrow \frac{1}{40}=(\mu -1)(\frac{1}{10}+\frac{1}{10})$
$\frac{1}{40}=(\mu -1)\left(\frac{2}{10}\right)$.