Question

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is $30cm$ and the refractive index of lens material is $1.5$, then the focal length of the lens is

Answer 1

Step 1: Given data

Radius of curvatures, $$\begin{gathered} R_1=\infty \\ {R}_2=-30cm \end{gathered}$$

Refractive index, $\mu =1.5$

Step 2: Find focal length

Applying Lens formula,

$\begin{array}{rcl}\frac{1}{f}& =& (\mu –1)[\frac{1}{R_1}–\frac{1}{R_2}]\\ \frac{1}{f}& =& (1.5-1)\left[\frac{1}{\infty }-\frac{1}{(-30)}\right]\\ \frac{1}{f}& =& 0.5/30\\ f& =& 60cm\end{array}$

Hence, the focal length of the lens is $60cm.$