Question

An electromagnetic wave of frequency 2.30 × 10^14 Hz propagates in carbon tetrachloride with a speed of 2.05 x 10^8 m/s. What is the wavelength of the wave in carbon tetrachloride? Show all work and include units of measure.
The index of refraction for water at 20° C is 1.333 and the index of refraction for air at 20° C is 1.00293. Find the angle of refraction for a ray of light that enters a bucket of water from air at an angle of 30.0° to the normal. Show all work and provide units of measure.

Answer 1

1. $8.91\cdot 10^{-7} m$

The wavelength of a wave is given by the formula

$\lambda=\frac{v}{f}$

where

v is the speed of the wave

f is the frequency

For the electromagnetic wave in this problem,

$f=2.30\cdot 10^{14}Hz$ is the frequency

$v=2.05\cdot 10^8 m/s$ is the speed of the wave

Substituting into the equation, we find

$\lambda=\frac{2.05\cdot 10^8 m/s}{2.30\cdot 10^{14}Hz}=8.91\cdot 10^{-7} m$

2.  $22.1^{\circ}$

The angle of refraction can be found by using Snell's law:

$n_i sin \theta_i = n_r sin \theta_r$

where

$n_i = 1.00293$ is the refractive index of the first medium (air)

$n_r = 1.333$ is the refractive index of the second medium (water)

$\theta_i = 30.0^{\circ}$ is the angle of incidence in air

Solving the equation for $\theta_r$, we find the angle of refraction of the light ray in water:

$\theta_r = sin^{-1} (\frac{n_i sin \theta_i}{n_r})=sin^{-1} (\frac{(1.00293)(sin 30^{\circ})}{1.333})=22.1^{\circ}$