Question

A plano-convex lens made of material of refractiv e index $\mu$ with radius of curvature $R$ is silvered on the curved side. How far away from the lens-mirror must you place a point object, so that the image coincides with the object?

• A. $\frac{R}{\mu}$
• B. $R$
• C. $\frac{R}{\mu-1}$
• D. $\mu R$

Answer 1

Answer: (A)

Due to silvering on curved surface,

lens acts like a concave mirror and its focal length f is given by
$\frac{1}{f}=\frac{2}{f_{e}}+\frac{1}{f_{m}}$
$=\frac{2}{R / \left(\mu-1\right)}+\frac{1}{R/2}$
$\Rightarrow f=\frac{R}{2\mu}$
Now, by mirror formula, we have
$\frac{1}{f}-\frac{1}{\upsilon} + \frac{1}{u} $
Here, $u=\upsilon=-x $
$\therefore \frac{2\mu}{R}=\frac{\left(-1\right)}{x}+\frac{\left(-1\right)}{x} $
$\Rightarrow \frac{2\mu}{R}=\frac{-2}{x} \,or\, x=\frac{-R}{\mu} $
So, distance of object is$\left(\frac{R}{\mu}\right)$ from the pole of silvered plano-convex lens