Question

A ray of light of frequency $5\times {10}^{14}Hz$ passes through a liquid. The wavelength of light measured inside the liquid is found to be $450nm.$ Calculate the refractive index of the liquid.

Answer 1

Step-1: Given data

Frequency, $\vartheta =5\times {10}^{14}Hz$

Wavelength of light inside the liquid, $\lambda =450nm=450\times {10}^{-9}m$

Speed of light in vacuum, $c=3\times {10}^8\frac{m}{s}$

Step-2: Calculating the refractive index of the liquid

Let v be the velocity of light in the medium.

As we know, $Velocity=Wavelength\times Frequency$

i.e. - $v=\vartheta \times \lambda$

$v=5\times {10}^{14}\times 450\times {10}^{-9}=2.25\times {10}^8\frac{m}{s}$

Now, the refractive index, $n=\frac{c}{v}=\frac{3\times {10}^8}{2.25\times {10}^8}=1.33$

Hence, the refractive index of the given liquid is $1.33$.