Question

A ray of light enters into benzene from air. If the refractive index of benzene is 1.50, by what percent does the speed of light reduce on entering the benzene?

Answer 1

Hint: To find out that by what percent the speed of light reduces on entering into the benzene we will understand the concept of refractive index. Then by using the given refractive index of benzene we will approach the answer with an easy formula.

Complete step-by-step answer:
Index of refraction is also called the refractive index. When the measure of the ray light bends and passes from one medium into another. In a vacuum if \[i\] is an angle of incidence of a ray, angle of refraction is $r$ and $n$ is the refractive index is defined as the sin of the angle of incidence’s ratio the sin of the angle of refraction i.e., $n = \dfrac{{\sin i}}{{\sin r}}$
Velocity of light c of a given wavelength in empty space is also equal to the refractive index which in a substance is divided by its velocity $v$.
Benzene can be written as or its symbol is $\mu $
It is given that the Refractive index of benzene ($\mu $ ) is = $1.50$
And the light initially was travelling in the air. The light enters benzene after travelling into air.
So, in benzene let the velocity of light = $v$
Then,
Benzene’s Refractive index is:
Formula used:
$\mu = \dfrac{c}{v}$
Now,
$
  v = \dfrac{c}{\mu } \\
  v = \dfrac{{3 \times {{10}^8}}}{{1.50}}m/s \\
  v = 2 \times {10^8}m/s \\
 $
So, the change in velocity of light is,
$
   \Rightarrow \,\,c - v \\
   \Rightarrow \,\,3 \times {10^8} - 2 \times {10^8} \\
   \Rightarrow \,\,1 \times {10^8}m/s \\
 $
Hence, the percentage in speed reduction will be:
$
   \Rightarrow \,\,\dfrac{{1 \times {{10}^8}}}{{3 \times {{10}^8}}} \times 100 \\
   \Rightarrow \,\,33.3\% \\
 $
Hence, the speed of light entering into benzene is reduced by 33%.

Note: Light when entered to denser medium from rarer medium, then its speed reduces. Refractive index of the medium is given by the two media (in the ratio of the speed of the light). More matter is provided by the denser medium by which the light can scatter and hence it will slowly travel in the dense medium.