Question

A double convex lens has a focal length of $50\text{cm}$. The radius of curvature of one refracting surface is double the other. Find the radii of curvature, if the refractive index of the material of the lens is $2$.

• A. $70\text{cm}$, $140\text{cm}$
• B. $62.5\text{cm}$, $125\text{cm}$
• C. $75\text{cm}$, $150\text{cm}$
• D. $25\text{cm}$, $50\text{cm}$

Answer 1

The correct option is C $75\text{cm}$, $150\text{cm}$


From the data given in the question,

$R_1=R,R_2=-2R,\mu =2,f=50\text{cm}$

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,

$\frac{1}{50}=(2-1)(\frac{1}{R}-\frac{1}{-2R})$

$\Rightarrow \frac{1}{50}=\frac{3}{2R}$

$\Rightarrow R=75\text{cm}$

$\therefore R_1=75\text{cm}$ and $R_2=150\text{cm}$

Hence, option (c) is the correct answer.