Question

The refractive index of a medium ‘x’ with respect to a medium ‘y’ is 2/3 and the refractive index of medium ‘y’ with respect to a medium ‘z’ is 4/3. Find the refractive index of medium ‘z’ with respect to medium ‘x’. If the speed of light in medium ‘x’ is $3\times {10}^{8}m/s$, calculate the speed of light in medium ‘y’.

Answer 1

Step 1: Given parameters

The refractive index of x with respect to y, $n_{xy}=\frac{2}{3}$……(1)

The refractive index of y with respect to z, $n_{yz}=\frac{4}{3}$

Step 2:Formula used

The refractive index of z with respect to x, $n_{zx}=\frac{n_z}{n_x}=\frac{n_z}{n_y}\times \frac{n_y}{n_x}$

This implies that $n_{zx}=\frac{1}{n_{yz}}\times \frac{1}{n_{xy}}$$=\frac{3}{4}\times \frac{3}{2}=\frac{9}{8}$

Hence refractive index of medium z with respect to medium x is, $n_{zx}=\frac{9}{8}$

Step 3: Calculating the speed of light in medium y

Let the speed of light in the medium ‘y’ be ‘V’ and the speed of light in the medium ‘x’ is ‘c’

From (1)

$$\begin{gathered} n_{yx}=\frac{n_y}{n_x}=\frac{3}{2} \\ \frac{y}{x}=\frac{3}{2}......\left(2\right) \end{gathered}$$

$\frac{C}{V}=\frac{3\times {10}^8}{V}...........\left(3\right)$

Equating (2) and (3), we get:

$V=2\times {10}^{8}m/s$

Hence the speed of light in medium y is 2 x 10⁸ m/s.