Question

When the plane surface of a plano-convex lens of refractive index $1.5$ is silvered, it behaves like a concave mirror with $f=30cm$.When its convex surface is silvered, it will behave like a concave mirror of focal length:

• A. $10cm$
• B. $20cm$
• C. $30cm$
• D. $45cm$

Answer 1

The correct option is C $30cm$

Let power of lens = $P_L$

Power of mirror=$P_M$

In case of silvering plane surface,

Refraction will take place through curve part twice,

And reflection will take place through plane part once.

$P=2P_L-P_M=2P_L=\frac{2}{f_L}=\frac{1}{30}c{m}^{-1}$( as power of plane mirror=0)

By lens maker formula,

$\frac{1}{f_L}=(\mu -1)\frac{1}{R}$

$\frac{1}{60}=\frac{1}{2R}$

$R=30cm$

$P_M=\frac{-100}{30}{m}^{-1}$

In case of silvering convex surface,

Refraction will take place via the plane part twice and

Reflection will take place through curve part once.

$P_L=0$ here as plane part won't refract like a lens.

$P=2P_L-P_M$=$-P_M=\frac{100}{30}{m}^{-1}$

$P=\frac{-1}{f}=\frac{-1}{30}c{m}^{-1}$

Focal length of the equivalent concave mirror = 30 cms.

Option $\text{C}$ is correct answer.