Question

Light enters from air to glass having a refractive index $1.50$ . What is the speed of light in the glass? The speed of light in a vacuum is:

Answer 1

Hint: You can start by defining the refractive index. Then also write the equation for the refractive index of a medium, i.e. $\eta = \dfrac{c}{v}$ . Then use this equation to find the value of \[{\eta _{air}}\] and \[{\eta _{glass}}\] . Then compare the value of \[{\eta _{air}}\] and \[{\eta _{glass}}\] to reach the solution.

Complete step by step answer:
 Refractive index – It is equal to the velocity of light divided by the velocity of that specific medium. In simple words, it is the measure of the amount of bending of light when it moves from one medium to another.
Let the refractive index of the glass be \[{\eta _{glass}}\] and the refractive index of air be \[{\eta _{air}}\].
We know that the equation for refractive index in terms of velocity of light is
$\eta = \dfrac{c}{v}$ (Equation 1)
Here, $\eta = $ Refractive index of the medium
$c = 3 \times {10^8}m/s = $ Speed of light in vacuum or air
$v = $ Speed of light in the medium
So, using equation 1 when light is traveling in the air
${\eta _{air}} = \dfrac{c}{{{v_{air}}}}$ (Equation 2)
And using equation 2 when light is traveling in the glass
${\eta _{glass}} = \dfrac{c}{{{v_{glass}}}}$ (Equation 3)
Dividing equation 2 by equation 3, we get
$\dfrac{{{\eta _{air}}}}{{{\eta _{glass}}}} = \dfrac{{\dfrac{c}{{{v_{air}}}}}}{{\dfrac{c}{{{v_{glass}}}}}}$
$ \Rightarrow \dfrac{{{\eta _{air}}}}{{{\eta _{glass}}}} = \dfrac{{{v_{glass}}}}{{{v_{air}}}}$
$ \Rightarrow {v_{glass}} = {v_{air}}\dfrac{{{\eta _{air}}}}{{{\eta _{glass}}}}$
We know that,
${v_{air}} = 3 \times {10^8}m/s$
${n_{air}} = 1$
${n_{glass}} = 1.50$ (Given)
So,
$ \Rightarrow {v_{glass}} = 3 \times {10^8} \times \dfrac{1}{{1.5}}$
$ \Rightarrow {v_{glass}} = 2 \times {10^8}m/s$
Hence, the speed of light in glass is $2 \times {10^8}m/s$ .

Note:
In the solution above, we considered that the refractive index of air is $1$ . The refractive index of air is $1$ because air or vacuum is considered as the standard for refractive index. The refractive index of every other medium is calculated relative to the refractive index of air. The speed of light is fastest in air or vacuum.