Question

Determine the speed, wavelength, and frequency of light from a helium-neon laser as it travels through zircon. the wavelength of the light from the laser is 632.8 nm in air and the index of refraction of zircon is 1.923.

Answer 1

(a) Speed

the speed of the helium-neon light in zircon is given by

$v=\frac{c}{n}$

where

$c=3.0 \cdot 10^8 m/s$ is the speed of light in vacuum (and in air)

$n=1.923$ is the refractive index of zircon

Substituting into the equation, we find

$v=\frac{3 \cdot 10^8 m/s}{1.923}=1.56 \cdot 10^8 m/s$

(b) Frequency

The wavelength of the light in air is:

$\lambda_0 =632.8 nm=632.8 \cdot 10^{-9} m$

The frequency of the light does not depend on the medium, so it is equal in air and in zircon. Therefore, we can calculate the frequency by using the speed of light in air and the wavelength in air:

$f_0 =\frac{c}{\lambda_0}=\frac{3 \cdot 10^8 m/s}{632.8 \cdot 10^{-9} m}=4.74 \cdot 10^{14} Hz$

and the frequency of the light in zircon is the same:

$f'=f_0 = 4.74 \cdot 10^{14} Hz$

(c) Wavelength

To calculate the wavelength of the light in zircon, we can use the relationship between speed of light in zircon and frequency:

$\lambda'=\frac{v}{f'}=\frac{1.56 \cdot 10^8 m/s}{4.74 \cdot 10^{14} Hz}=3.29 \cdot 10^{-7} m=329 nm$