Question

The graph of $\sin i$ versus $\sin r$ for certain materials is given below. Identify the curve which is not possible for a given material. Assume the first medium to be air.
($i$ and $r$ are angle of incidence and refraction)

• A. I
• B. II
• C. III
• D. All the above

Answer 1

The correct option is A I

We know that, by Snell's law,
$\frac{\sin i}{\sin r}=\mu$
$[$when first medium is air$]$
Also, speed of light in any medium,
$v=\frac{c}{\mu }$
We know that the speed of light cannot be greater than $c$.
Thus, $v=\frac{c}{\mu }\le c$
$\Rightarrow \mu \ge 1$
From the graph, the slope of the curve represents the refractive index $\left(\mu \right)$.

For curve $\text{I}$,
Slope, $m=\mu =\tan {30}^{\circ }=\frac{1}{\sqrt{3}}<1$
For curve $\text{II}$,
$m=\mu =\tan {45}^{\circ }=1$
For curve $\text{III}$,
$m=\mu =\tan {60}^{\circ }=\sqrt{3}>1$
Hence, curve $\text{I}$ is not possible.

Why this question? It tests your basic understanding about refractive index $\left(\mu \right)$. Caution: $\mu$ is always greater than or equal to 1. Tips: Slope of $\sin i$ vs $\sin r$ graph gives $\mu$.