Question

A double convex lens has a focal length of $40\text{cm}$. If the radius of curvature of its refracting surfaces are $10\text{cm}$ and $20\text{cm}$, find the refractive index of the material of the lens.

• A. $\frac{4}{3}$
• B. $\frac{5}{3}$
• C. $\frac{7}{5}$
• D. $\frac{7}{6}$

Answer 1

The correct option is D $\frac{7}{6}$

From the data given in the question,

$R_1=10\text{cm},R_2=-20\text{cm},$
$($As for a bi-convex lens, $R_1$ is positive and $R_2$ is negative$)$
$f=40\text{cm,}\mu =?$

According to lens maker's formula,

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

Substituting the given data we get,

$\frac{1}{40}=(\mu -1)(\frac{1}{10}-\frac{1}{-20})$

$\Rightarrow \frac{1}{40}=(\mu -1)\frac{3}{20}$

$\Rightarrow \mu -1=\frac{1}{6}$

$\Rightarrow \mu =\frac{7}{6}$

Hence, option (d) is the correct answer.