Question

A plano-convex lens has refractive index $1.5$ and radius of curvature $50cm$. What is focal length of lens?

• A. 100 cm
• B. 200 cm
• C. 178 cm
• D. 150 cm

Answer 1

Answer: (A)

If $R_1$ and $R_2$ are the radii of curvature of first and second refracting
surfaces of a thin lens with optical centre $C$ of focal length $f$ and refractive index $\mu$ then according to lens Makers formula
$\frac{1}{f}=(\mu -1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
where $\mu$ is refractive index of material of lens. with respect to surrounding medium.
For plano-convex lens, $R_1=50cm,R=\infty$ (for plane surface)
$\frac{1}{f}=(1.5-1)\left(\frac{1}{50}-\frac{1}{\infty }\right)$
or $\frac{1}{f}=0.5\times \frac{1}{50}$ or
$f=\frac{50}{0.5}=100cm$