Question

The focal length of a plano-convex glass lens is $20\text{cm}$ $({\mu }_g=1.5)$. The plane face of glass lens is silvered. An illuminating object is placed at a distance of $60\text{cm}$ from the lens on its axis along the convex side. Then the distance (in $\text{cm}$) of the image is

• A. $20$
• B. $30$
• C. $40$
• D. $12$

Answer 1

The correct option is D $12$

We know that,

Power of silvered lens will be
$$P=2P_L+P_m$$
where , $P_L$ is power of lens and $P_m$ is power of mirror.

For plane mirror, $P_m=0$ $(\because f=\infty )$

and , $P_L=\frac{1}{f_L}$

Substituting the given data we get,

$P_L=\frac{1}{0.2}=5\text{D}$

$\therefore P=10\text{D}$

Effective focal length $\left(f\right)=-\frac{1}{10}=-0.1\text{m}\text{or}-10\text{cm}$

Using mirror formula,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Substituting the data obtained,

$\frac{1}{v}+\frac{1}{-60}=\frac{1}{-10}$

$\Rightarrow \frac{1}{v}=\frac{1}{60}-\frac{1}{10}$

$\Rightarrow v=12\text{cm}$

Hence, option (d) is the correct answer.

Why this question? Note:- The effective focal length of silvered lens is given by $$\frac{1}{f}=\frac{1}{f_m}-\frac{2}{f_L}$$