Question

If in a plano-convex lens, radius of curvature of convex surface is $10cm$ and the focal length of the lens is $30cm,$ the refractive index of the material of the lens will be :

• A. 31.5
• B. 1.5
• C. 1.66
• D. 1.33

Answer 1

The correct option is D 1.33

$\begin{array}{c}Le{n}^{\prime }smakersformula,\\ \frac{1}{f}=\left(\mu -1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\\ Inplano-convexlens,\\ R_2=\infty \\ \frac{1}{30}=\left(\mu -1\right)\left(\frac{1}{10}-\frac{1}{\infty }\right)\\ \Rightarrow \frac{1}{3}=\mu -1\\ \therefore \mu =\frac{4}{3}=1.33\end{array}$

Hence,Option $D$ is correct.