Answer:
Angle of refraction = 28.9 degrees
Explanation:
We can use Snell's law to solve this problem.
[tex]n_1* sin(\alpha _1)=n_2 * sin(\alpha _2)[/tex]
where the subindex 1 refers to one media (let's say air in our case), and the subindex 2 refers to the other media (water in our case)
[tex]n_1[/tex] and [tex]n_2[/tex] are the respective indeces of refraction for the two media.
Recall that the index of refraction for air is 1, while the index of refraction for water is around 1.333.
We know the angle if incident light in air; 40 degrees, so we need to solve for first for the [tex]sin(\alpha _2)[/tex] in the equation, and then find what angle [tex]\alpha _2[/tex] is by using the arc-sin function:
[tex]n_1* sin(\alpha _1)=n_2 * sin(\alpha _2)\\1 * sin(40)= 1.333 * sin(\alpha _2)\\sin(\alpha_2)=\frac{sin(40)}{1.333} = 0.48221\\\\alpha _2 =arcsin(0.48221)= 28.9^o[/tex]
