Question

Monochromatic light of wavelength $589$nm is incident from air on a water surface. If $\mu$ for water is $1.33$, find the wavelength, frequency and speed of the refracted light.

Answer 1

wavelength $\lambda =589nm=589\times {10}^{-9}m$

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

Refractive index of water, $\mu$ = 1.33

The frequency of light does not depend on the property of the medium in which it is travelling. Hence, the frequency of the refracted ray in water will be equal to the frequency of the incident or reflected light in air.

So Refracted frequency, $\nu =\frac{c}{\lambda }=5.09\times {10}^{14}Hz$

Speed of light in water is related to the refractive index of water as:

$v=\frac{c}{\mu }=2.26\times {10}^8$ m/s.Wavelength of light in water is given by the relation${\lambda }_1=\frac{v}{\nu }=444\times {10}^{-9}m=444nm$