Question

Find the focal length of the lens shown in figure. The radius of curvature is $R=10\text{cm}$ and the refractive index of material of the lens is $\frac{3}{2}$.

• A. $+20\text{cm}$
• B. $-30\text{cm}$
• C. $-15\text{cm}$
• D. $+10\text{cm}$

Answer 1

The correct option is D $+10\text{cm}$

Lens maker's formula for convex lens if object is at infinity,
$\frac{1}{f}=(\frac{{\mu }_2}{{\mu }_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$
Here,
${\mu }_2=\frac{3}{2},{\mu }_1=1$, $R_1=+10\text{cm}$ and $R_2=-10\text{cm}$


$\Rightarrow \frac{1}{f}=(\frac{3}{2}-1)(\frac{1}{10}-\frac{1}{-10})$

or, $\frac{1}{f}=\frac{1}{2}\left(\frac{2}{10}\right)$

$\therefore f=+10\text{cm}$

Why this question? Tip: In such questions, be very careful with the sign convention of $R_1$ and $R_2$. It is recommended to select positive in the direction of incidence.