Question

A convex lens made of glass, with refractive index $\frac{3}{2}$, is placed in a medium of refractive index $\frac{5}{2}$. A parallel beam of light entering the lens ________.

• A. diverges
• B. converges
• C. undergoes no refraction
• D. comes out as a parallel beam by itself

Answer 1

The correct option is A

diverges

Step 1: Analyzing given data:
Refractive Index of the lens $\left({\mu }_L\right)=\frac{3}{2}$
Refractive Index of the medium: $\left({\mu }_M\right)=\frac{5}{2}$
Step 2: Finding the nature of the lens:
According to the lens maker's formula;
$\frac{1}{f}=\left(\frac{{\mu }_L-{\mu }_M}{{\mu }_M}\right)\left[\frac{1}{R_1}-\frac{1}{R_2}\right]$ (where f is the resultant focal length and $R_1$, $R_2$ are the radii of curvature)
Let $\left[\frac{1}{R_1}-\frac{1}{R_2}\right]=A$ (because radii of curvature will be constant)
$\Rightarrow \frac{1}{f}=\left(\frac{{\mu }_L-{\mu }_M}{{\mu }_M}\right)A$
Here, we are given that: ${\mu }_L=\frac{3}{2}$ and ${\mu }_M=\frac{5}{2}$
$\Rightarrow {\mu }_M>{\mu }_L$
$\Rightarrow {\mu }_L-{\mu }_M$ will be negative.
$\Rightarrow$$f$ will be negative.
Since $f$ is negative, the lens will act as a diverging lens.

Thus, a parallel beam of light entering the lens diverges.
Hence, Option (A) is the correct answer.