Question

The refractive index of water is 1.33. What is the angle of refraction if light (in air) strikes water at an angle of incidence of a 24°?

Answer 1

It is `17^\circ`.

Explanation:

The Snell's law tell us that when you have two medium with refraction index `n_1` and `n_2` the equation is

`n_1sin(theta_1)=n_2sin(theta_2)`

with `theta_1` and `theta_2` the angle in the first medium and the angle in the second medium respectively.

For us the initial angle is `theta_1=27^\circ` and `n_2=1.33`.
In order to calculate `\theta_2` we need to know `n_1`. We assume that `n_1=1` for air, even if it depends on the density and temperature of it.

Then our equations is

`1*sin(27^\circ)=1.33*sin(theta_2)`

`theta_2=arcsin(sin(27^\circ)/1.33)\approx17^\circ`.