Question

A bi-convex thin lens is prepared from glass $(\mu =1.5)$, the two bounding surfaces having equal radii of $25\text{cm}$ each. One of the surface is silvered from outside. Where should an object be placed before this lens such that the image is formed at the object position itself?

• A. $5\text{cm}$
• B. $-7\text{cm}$
• C. $-12.5\text{cm}$
• D. $-3\text{cm}$

Answer 1

The correct option is C $-12.5\text{cm}$

If ray from the object falls normally on the silvered surface it reflects back and forms an image on the object itself.


The AB should appear to come from the centre $C_2$ of the second surface. Thus due to the refraction at the first surface, vitual image of $\text{O}$ is formed at $C_2$.

For this case,

$v=-25\text{cm},R=25\text{cm},{\mu }_1=1,{\mu }_2=1.5$

We have,

$\frac{{\mu }_1}{v}-\frac{{\mu }_2}{u}=\frac{{\mu }_1-{\mu }_2}{R}$

$\frac{1.5}{-25}-\frac{1}{u}=\frac{1.5-1}{25}$

$\Rightarrow \frac{1}{u}=\frac{-1.5}{25}-\frac{0.5}{25}$

$\Rightarrow u=-12.5\text{cm}$

Hence, option (c) is the correct answer.