A monochromatic electromagnetic wave of frequency $5\times 10^{14}\text{Hz}$ propagates in glass whose refractive index is $n=1.5$. Calculate (i) the speed of the wave in glass and (ii) its wavelength in glass.

Step-by-step solution

1. Write the speed of light in vacuum as $c=3.0\times 10^8{\text{m s}}^{-1}$.
2. In a medium of refractive index $n$, the speed is $v=\frac{c}{n}$; substitute $n=1.5$ to get $v=\frac{3.0\times 10^8}{1.5}=2.0\times 10^8{\text{m s}}^{-1}$.
3. The wavelength in the medium is $\lambda =\frac{v}{f}$, where $f=5\times 10^{14}\text{Hz}$.
4. Insert the values: $\lambda =\frac{2.0\times 10^8}{5\times 10^{14}}=4.0\times 10^{-7}\text{m}$.
5. Thus the speed and wavelength are $2.0\times 10^8{\text{m s}}^{-1}$ and $4.0\times 10^{-7}\text{m}$ respectively.

Concept tested: Speed and wavelength in a dielectric

Published 9 September 2026 · How this solution was prepared and checked