Question

Radii of curvature of a converging lens are in the ratio $1:2$. Its focal length is $6$cm and refractive index is $1.5$. Then its radii of curvature are _________ respectively.

• A. $9$cm and $18$cm
• B. $6$cm and $12$cm
• C. $3$cm and $6$cm
• D. $4.5$cm and $9$cm

Answer 1

Answer: (D)

$4.5$cm and $9$cm

Given : $R_1:R_2=1:2$ $f=6$ cm $\mu =1.5$

$⟹$ $R_2=2R_1$---------------(1)

Using lens maker formula, $\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{-R_2})$

OR $\frac{1}{6}=(1.5-1)(\frac{1}{R_1}+\frac{1}{2R_1})$

OR $\frac{1}{6}=\left(0.5\right)(\frac{3}{2R_1})$ $⟹R_1=4.5$ cm
On putting the value of $R_1$ in equation (1):

$⟹R_2=2\times 4.5=9$ cm
Hence the correct option is $\left(D\right)$