Question

A planoconvex lens, when silvered in the plane side behaves like a concave mirror of focal length $30$ cm. However, when silvered on the convex side it behaves like a concave mirror of focal length $10$ cm. Then the refrective index of its material will be

• A. $3.0$
• B. $2.0$
• C. $2.5$
• D. $1.5$

Answer 1

Answer: (D)

$1.5$

We know, $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

If the object is placed at a distance of 20 cm from the lens, its image will be formed at the same place,

$f_{lens}=2\times f_{mirror}=2\times 30=60cm$

Given, $v=-R_{lens};u=-20cm$

$\therefore \frac{1}{60}=\frac{1}{R_{lens}}+\frac{1}{20}$

or $\frac{1}{R_{lens}}=\frac{1}{20}-\frac{1}{60}=\frac{1}{30}$

Now, $\frac{1}{f}=\frac{(\mu -1)}{R}$

$\Rightarrow \frac{1}{60}=\frac{(\mu -1)}{30}$

$\therefore \mu =1.5$

and radius of curvature of lens $=30cm$.