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=(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=(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) ((n_i sin \theta_i)/(n_r))=sin^(-1) (((1.00293)(sin 30^(\circ)))/(1.333))=22.1^(\circ)`