Question

A point object is placed at a distance of $20cm$ from a thin plano-convex lens of focal length $15cm$, if the plane surface is silvered. The image will form at :

• A. $60cm$ left of $AB$
• B. $30cm$ left of $AB$
• C. $12cm$ left of $AB$
• D. $60cm$ right of $AB$

Answer 1

The correct option is C $12cm$ left of $AB$

Formula for focal length for a lens is

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$ where f=15cm,$R_2=\infty$,$R_1=?$,$\mu =1.5$

Now solving the equation we have $R_1=15/2cm$

After silvering of lens from one side the system starts acting as a mirror of focal length given by

$\frac{1}{f}=\frac{2\mu }{R_2}-\frac{2(\mu -1)}{R_1}$

$\Rightarrow \frac{1}{v}+\frac{1}{u}=\frac{2\mu }{R_2}-\frac{2(\mu -1)}{R_1}$

$\Rightarrow \frac{1}{v}+\frac{1}{-20}=\frac{2\times 1.5}{\infty }-\frac{2(1.5-1)\times 2}{15}\Rightarrow v=-12cm$