Question

A part of the path of a light ray travelling inside a liquid is shown in the given figure.

Based on the given diagram, select the most appropriate statement regarding the refracting index of the liquid.

• A. The liquid has a constant value of refracting index.
• B. Refracting index of liquid decreases from top to bottom.
• C. Refracting index of liquid increases at a steady rate from top to bottom.
• D. Refracting index of liquid is first increasing then decreasing.

Answer 1

The correct option is C Refracting index of liquid increases at a steady rate from top to bottom.


From the ray diagram, we can see that angle of incidence at layer $PMN$ of the liquid attained such a value which facilitated $\text{TIR}$. Thus, light was travelling from an optical rarer liquid layer to an optical denser liquid layer.

$\Rightarrow$ From the path $AM$, it is evident that light ray is continuously bending towards the normal.

$\therefore$ RI of light is increasing continuously from top to bottom.
Similarly, during the journey of reflected ray (path $MB$), ray is getting away from normal continuously.

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

Why this question? It intends to bring your attention to behaviour of variable refracting index liquid. Tip: observe the smooth variation in curvature of path of light ray, it suggests steady variation in refracting index of liquid.