Question

A ray of light incident on a medium angle of incidence i and refracted in one second medium with angle of refraction r .the graph of sin i versus sin r is as shown . Find the ratio of velocity of light in the first medium to velocity of light in the second medium

Answer 1

No graph is attached with the question. The below, however can be used for any appropriate graph given.

Note that sin(i) is assumed to be taken on the y-axis, and sin(r) on the x-axis.

Snell's law (IIRC), states that:

$sin(r) = \mu sin(i)$

Hence, the graph of sin(i) vs sin(r) must be a straight line, with the slope equal to $\frac{1}{\mu}$.

Here, $\mu$ is the relative refractive index of medium 1 with respect to medium 2.

By definition, $\mu$ is the ratio of speed of light in medium 2 with respect to medium 1, or, $\mu = \frac{v_{2}}{v_{1}}$.

So, the slope of the graph:

$m = \frac{1}{\mu} = \frac{1}{\frac{v_{2}}{v_{1}}} = \frac{v_{1}}{v_{2}}$

Hence the slope of the graph, that is, tanθ (where θ is inclination) is the required ratio.