Question

A thin plano-convex lens acts like a concave mirror of focal length $0.2\, m$ when silvered from its plane surface. The refractive index of the material of the lens is $1.5$. The radius of curvature of the convex surface of the lens will be

• A. 0.1 m
• B. 0.75 m
• C. 0.4 m
• D. 0.2 m

Answer 1

Answer: (D)

After silvering the plane surface, plano-convex lens behaves as a concave mirror of focal length
$\frac{1}{F}=\frac{2}{f_{\text {lens }}}$
But $F=0.2\, m$
$\therefore f_{\text {lens}}=2 F=2 \times 0.2=0.4\, m$
Now, from lens maker's formula
$\frac{1}{f_{\text {lens }}}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
$\therefore \frac{1}{0.4}=(1.5-1) \times \frac{1}{R_{1}}$
$\left[\because R_{2}=\infty\right]$
$\Rightarrow R_{1}=0.5 \times 0.4=0.2\, m$