Question

A plano convex lens is made up of flint glass

(refractive index = 1.65) and its convex side has a

curvature of radius 33 cm. Find the focal length of the

plano convex lens if its convex surface is silvered.

A) 25.4 cm

B) 5 cm

C) 16.5 cm

D) 10 cm

​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Refractive index $(\mu)$ = 1.65
• Radius of curvature of Convex side (R) = 33cm

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Focal length of the plano convex lens if its convex surface is silvered.

━━━━━━━━━━━━━━━━━━━━━━━━━━━

❏ When Curved Surface is silvered then -

$\implies{\sf P = 2P_L + P_M}$

$\implies{\sf \dfrac{1}{F}=\dfrac{2}{f_{\ell}}+\dfrac{1}{f_m} }$

$\implies{\sf \dfrac{1}{F}=\dfrac{2(\mu-1)}{R}+\dfrac{2}{R} }$

$\implies{\sf \dfrac{1}{F}=\dfrac{2\mu}{R}}$

$\color{red}\blacksquare\underline{\boxed{\sf F=\dfrac{R}{2\mu}}}$

$\implies{\sf F =\dfrac{33}{2×1.65}}$

$\implies{\sf F=\dfrac{33}{3.3}}$

$\color{red}\implies{\sf F=10cm}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Option (D) 10cm

When Curved surface is silvered then focal Lenght will be $\color{red}{\sf 10cm}$