Question

What is the speed of light in glass if the index of refraction of the glass is \[1.63?\]
A. \[4.89 \times {10^8}m/s\]
B. \[5.43 \times {10^{ - 9}}m/s\]
C. \[3.00 \times {10^8}m/s\]
D. \[1.84 \times {10^8}m/s\]
E. \[4.63 \times {10^8}m/s\]

Answer 1

Hint: We need to know the refractive index of glass or any medium and the velocity of light through glass or through the same medium.
Relation between refractive index of a medium, speed of light, and velocity of light through the same medium can be $n = \dfrac{c}{v}$

Complete step by step answer:
We need to look up the index of refraction for glass \[\left( {one{\text{ }}source{\text{ }}is\;Index{\text{ }}of{\text{ }}Refraction} \right).\]
It is likely to be about \[1.5{\text{ }}to{\text{ }}1.7\] depending on the specific substances in the glass. This index is denoted n. The speed of light in a substance with index of refraction n is \[c/n\] where c is the speed of light in a vacuum or \[c\; = {\text{ }}2.99792458 \times {10^8}{\text{ }}m/s.\]
It is only wavelengths that are absorbed by orbital electrons, and propagated by massive particles, that travel at lower speeds. And these are strongly dependent on wavelength. So the whole range of values, depending on wavelength, and the dopants in the glass.

Refractive index is the ratio of the velocity of light in a vacuum to its velocity in a specified medium.
$n = \dfrac{c}{v}$
\[n = refractive{\text{ }}index\]
\[c = refractive{\text{ }}index{\text{ }}of{\text{ }}light{\text{ }}in{\text{ }}air{\text{ }}medium\]
\[v = refractive{\text{ }}index{\text{ }}of{\text{ }}light{\text{ }}in{\text{ }}glass{\text{ }}medium\]
Refractive index of glass is \[n = 1.63\]
So,
$
  {v_{glass}} = \dfrac{c}{n} \\
  {v_{glass}} = \dfrac{{3 \times {{10}^8}}}{{1.63}} \\
  {v_{glass}} = 1.84 \times {10^8}m/s \\
 $

So, the correct answer is “Option D”.

Note:
We can use $
  n = \dfrac{c}{v} \\
   \Rightarrow c = n.v \\
 $
For speed of light in all media is constant so if we know the refractive index of glass, any other medium and velocity of light through that medium we can find the velocity of light through glass
$
  c = n.v \\
  {n_{glass}}.{v_{glass}} = {n_{medium1}}.{v_{medium1}} \\
 $
If we know the refractive index of air and velocity of light through air then,
${n_{glass}}.{v_{glass}} = {n_{air}}.{v_{air}}$
Refraction is an effect that occurs when a light incident at an angle away from the normal passes a boundary from one medium into another in which there is a change in velocity of the light in air into glass in which it moves more slowly.