Question

What is the angle of refraction if a ray of light passes from water into air at an angle of 30 degrees?

Answer 1

One problem solving strategy that I find very useful in answering a question like this is GRASS.

G - what am I Given? Assign each value to a number.
`n_1` = the index of refraction in the first substance, which is water (1.33)
`Theta_1` = the angle of incidence (`30^o`).
`n_2` = the index of refraction in the second substance, which is air (1.0003)

R - what am i Required to find? This is my unknown (`Theta_2`).

A - what formula do I need to use? Do I need to manipulate the equation to isolate my unknown value?
To answer a question like this, use Snell's Law (`n_1 sin Theta_1 = n_2 sin Theta_2`). The unknown in this problem is `Theta_2`, which should be isolated.

S - Solve.
`sin Theta_2 = (n_1 * sin Theta_1) / n_2`
`sin Theta_2 = (1.33 * sin 30^o) / 1.0003`
`sin Theta_2 = 0.6648`
`Theta_2 = sin^-1 0.6648`
`Theta_2 = 41.66^o`

S - Significant digits.
Since `30^o` only contains 2 significant digits, the answer needs to be rounded to 2 significant digits, which means the angle of refraction in air is `42^o`.