In Fig. 35-23, three pulses of light— $\mathit{a}$, $\mathit{b}$, and $\mathit{c}$—of the same wavelength are sent through layers of plastic having the given indexes of refraction and along the paths indicated. Rank the pulses according to their travel time through the plastic layers, greatest first.

Refractive index of the medium through which pulse $a$ passes is$1.6$.

Refractive index of the medium through which pulse$b$passes is$1.5$.

Refractive index of the medium through which pulse $c$ passes is$1.55$ .

$\mathit{v}$The velocity of light in a medium having a refractive index$\mathit{c}$is given by

$\mathit{v}\mathbf{=}\frac{\mathbf{c}}{\mathbf{n}}$ .....(1)

Here, $\mathit{c}$is the velocity of light in a vacuum, is the velocity of light in the substance,and $\mathit{n}$ in the index of refraction.

From equation (1), the velocity of pulse $a$ in the first layer is

$V_a=\frac{c}{1.6}$

Let the thickness of each layer be$d$ . Thus, the time taken by the first pulse to cross the layer is

$\begin{array}{l}{t}_a=\frac{d}{c/1.6}\\ =\frac{1.6d}{c}\end{array}$

Similarly, the time taken by the second pulse to cross the layer is,

$t_b=\frac{1.5d}{c}$

And the time taken by third pulse to cross the layer is,

$t_c=\frac{1.55d}{c}$

Hence, the rank of the pulses according to their travel time through the plastic layers, greatest first is$t_a>t_c>t_b$ .