A monochromatic electromagnetic wave of frequency $6\times 10^{14}\text{Hz}$ travels in water whose refractive index is $n=1.33$. Find (i) the speed of the wave in water and (ii) its wavelength in water.

Step-by-step solution

1. Write the speed of an EM wave in a medium as $v=\frac{c}{n}$, because the refractive index $n$ reduces the speed by a factor $n$.
2. Substitute $c=3.00\times 10^8{\text{m s}}^{-1}$ and $n=1.33$ to obtain $v=\frac{3.00\times 10^8}{1.33}=2.25\times 10^8{\text{m s}}^{-1}$.
3. Use the relation between speed, frequency and wavelength: $\lambda =\frac{v}{f}$.
4. Insert $v=2.25\times 10^8{\text{m s}}^{-1}$ and $f=6\times 10^{14}\text{Hz}$ to get $\lambda =\frac{2.25\times 10^8}{6\times 10^{14}}=3.38\times 10^{-7}\text{m}$.
5. State both the speed and the wavelength as the final answer.

Concept tested: Wavelength and speed in a refractive medium

Published 8 September 2026 · How this solution was prepared and checked