Question

The refractive index of diamond is 2.42 and the speed of light in air is \[3 \times {10^8}m{s^{ - 1}}\] calculate the speed of light in diamond.

Answer 1

Hint: One of the most important properties of the wave is refraction. In this phenomenon, the rays of light get bent when they pass through different mediums and when we provide the ratio of the speed of light (wave) in various media, it is called a refractive index.

Complete step by step solution:
The refractive index \[\left( n \right)\] is given by,
\[n = \dfrac{{Speed\;of\;light\,\;in\;vacuum}}{{Speed\,\,of\;light\;in\,\;medium\,}}\]
Refractive index of diamond = 2.42
Speed of light = \[3 \times {10^8}m{s^{ - 1}}\]
Speed of the light in diamond = ?
As we all know that,
\[n = \dfrac{{Speed\,of\,light\,in\,vacuum}}{{Speed\,\,of\,Light\,in\,medium\,}}\]
\[n = \dfrac{c}{V}\]
\[2.42 = \dfrac{{3 \times {{10}^8}}}{{speed\,\,of\,\,light\;in\;medium}}\]
\[
  Speed\,\,of\,light\;in\;medium\, = \,\dfrac{{3 \times {{10}^8}}}{{2.42}} \\
   = 1.25\, \times {10^8}\,m/s \\
 \]

Note: Speed of light in vacuum is the fastest speed in the universe that is \[3 \times {10^8}\;m/s\]
Refractive index is the ratio of the velocity of light in a vacuum to velocity of light in media.