Question

Find the radius of curvature of the simple microscope's lens whose maximum magnifying power is $6$. (Refractive index of glass used, ${\mu }_l=1.5)$

• A. $2\text{cm}$
• B. $6\text{cm}$
• C. $3\text{cm}$
• D. $5\text{cm}$

Answer 1

The correct option is D $5\text{cm}$

Given, $m=6$

Maximum magnifying power,

$m=1+\frac{D}{f}$

$\Rightarrow 6=1+\frac{25}{f}$

$\therefore f=5\text{cm}$

Now, using lens maker formula,

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

Let $R$ be the radius of curvature of the microscope's lens,

$\frac{1}{5}=\frac{1.5-1}{1}(\frac{1}{R}-(-\frac{1}{R}))$

$\Rightarrow \frac{1}{5}=0.5\times \frac{2}{R}$

$\therefore R=5\text{cm}$

Hence, $\left(D\right)$ is the correct answer.