Question

If the velocity of light in vacuum is $3\times {{10}^{8}}m{{s}^{-1}}$, the time taken (in nanosecond) to travel through a glass plate of thickness $10cm$ and refractive index $1.5$ is:
$\begin{align}
  & A. 0.5 \\
 & B. 1.0 \\
 & C. 2.0 \\
 & D. 3.0 \\
\end{align}$

Answer 1

Hint: When light passes through glass, it gets knocked around and bumps into all kinds of molecules and electrons. So whenever it's traveling or passing through the glass plate, the optical path it traversed will be different from the geometrical path.

Complete step by step answer:
First of all let us discuss what the optical path actually means. The path that a light ray follows as it travels through an optical medium or a system is sometimes known as the optical path. Here it is given that velocity with which the light travels in the vacuum is given as
$v=3\times {{10}^{8}}m{{s}^{-1}}$
The thickness of the glass plate is,
$d=10cm$
And also the refractive index of the glass plate will be
$n=1.5$
As we know the optical path is given by the equation,
$\mu =\dfrac{C}{V}$
And the time taken to travel in the glass plate is
$t=\dfrac{d}{V}$
Substituting V from the refractive index equation will give,
$t=\dfrac{d}{\dfrac{C}{\mu }}$
Substituting this values in the equation,
\[t=\dfrac{10 \times 10^{-2}}{\dfrac{3\times {{10}^{8}}}{1.5}}\]
\[t=0.5\times {{10}^{-9}}s=0.5ns\]

So, the correct answer is “Option A”.

Note: The optical path length as described in optics is the length of the path traversed multiplied by the refractive index of the medium. Here the path traversed is the geometrical path length which is being multiplied with the refractive index of a medium. Refractive Index or the Index of Refraction is a value measured from the ratio of the speed of light in a vacuum to that in a second medium of more density. The refractive index variable is most generally symbolized by the notations like n or n' in the complete explanations and mathematical equations.