Question

Light enters from air to glass having a refractive index of $1.50$. What is the speed of light in the glass? The speed of light in vacuum is $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.

Answer 1

Step 1. Given data:

Speed of light in vacuum $\left(c\right)$ = $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Speed of light in any medium = speed of light in vacuum. (Speed of light is independent of any medium or vacuum)

Hence, the speed of light in air $\left(c\right)$ = $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Refractive index of glass $\left(n_g\right)$ = $1.5$

Step 2. Formula used:

Speed of light in a glass $\left(v\right)$ = Speed of light in air $\left(c\right)$ / Refractive index of glass $\left(n_g\right)$

Step 3. Calculations:

As we know, Speed of light in a glass $\left(v\right)$ = Speed of light in air $\left(c\right)$ / Refractive index of glass $\left(n_g\right)$

Or $v=\frac{c}{n_g}=\frac{3\times {10}^8}{1.5}=2\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Hence, the speed of light in glass will be $2\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.