Question

A point object is placed in front of an equi- convex lens, of refractive index $1.5$ and focal length $20\text{cm}$ , at a distance $10\text{cm}$ from the lens. If the farther side of the lens from the object is silvered then find the image distance from the lens

• A. $5\text{cm}$
• B. $10\text{cm}$
• C. $50\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is B $10\text{cm}$

Using lens maker's formula, for equiconvex lens, $f_l=\frac{R}{2(\mu -1)}\Rightarrow R=f_l=20\text{cm}$

After one side is silvered, the focal length of the mirror is given by
$f_m=\frac{R}{2}=-10\text{cm}$

Now considering as a combination of lens and mirror,

To form an image, light has to travel through the lens two times,
So, $P_{eff}=P_M+2P_L$

$\frac{1}{f_{eq}}=-(\frac{1}{10}+\frac{2}{20})=-\frac{1}{5}\Rightarrow f_{eq}=-5\text{cm}$ (as a combination, it acts as a concave mirror)

Using mirror formula , $(\frac{1}{u}+\frac{1}{v})=\frac{1}{f_{eq}}$

$u=-10\text{cm}\Rightarrow \frac{1}{-10}+\frac{1}{v}=\frac{1}{-5}$

we get, $v=-10\text{cm}$

Hence, option $\left(b\right)$ is correct.