A monochromatic light beam of frequency propagates from vacuum into a liquid of…

PHYSICS · Multi-part · CBSE · Physics · Light — Reflection and Refraction · Light — Reflection and Refraction

Problem

A monochromatic light beam of frequency

\nu

propagates from vacuum into a liquid of refractive index

n

. (i) Derive an expression for the wavelength

\lambda

of the light inside the liquid in terms of its wavelength in vacuum

\lambda_0

and the refractive index

n

. (ii) Using the result of part (i), show that the ratio

\omega/k

for the light inside the liquid equals

c/n

, where

c

is the speed of light in vacuum. (iii) For

n = 1.33

and

\nu = 6.0\times10^{14}\,\text{Hz}

, calculate (a) the angular frequency, (b) the wave number and (c) the phase velocity of the wave inside the liquid.