Question

A lens is made up of two identical spherical surfaces having radius of curvature and refractive index $20\text{cm}$ and $1$ respectively. If the lens is placed in a medium having refractive index $2$, what will be the nature of the lens?

• A. Diverging lens
• B. Converging lens
• C. Both coverging and diverging lens
• D. None of these

Answer 1

The correct option is A Diverging lens


For the above given diagram, we need to find the focal length of the lens.
Using Lens maker's formula

$\frac{1}{f}=(\frac{{\mu }_2}{{\mu }_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$

Here, ${\mu }_1=2;{\mu }_2=1$

$R_1=+20\text{cm};R_2=-10\text{cm}$

$\frac{1}{f}=(\frac{1}{2}-1)(\frac{1}{20}-\frac{1}{(-20)})$

$\frac{1}{f}=-0.5\left(\frac{2}{20}\right)$

$\therefore f=-20\text{cm}$

Negative focal length means this lens will behave like a diverging lens (concave lens).

Hence, option $\left(a\right)$ is correct.