Question

At what angle above the horizontal is the sun if sunlight reflected from the surface of a calm lake is completely polarized? Note that the angle asked for is the angle from the surface

Answer 1

θ = 36.94°

Explanation:

Brewster's law for polarization states that; tan(θ_p) = n2/n1

Where ;

θ_p is the polarizing angle

n1 is the index of refraction of first material

n2 is the index of refraction of second material

Now, our first material here is air while second material is water.

Index of refraction of water = 1.33 while index of refraction of air is 1

Thus,

tan(θ_p) = n2/n1 = 1.33/1

tan(θ_p) = 1.33

(θ_p) = tan^(-1)1.33

(θ_p) = 53.06°

Now, polarizing angle is the angle of incidence for which all the reflected light is polarized and it's above the vertical. Thus to get the angle to the horizontal, it will be;

θ = 90° - (θ_p) = 90° - 53.06° = 36.94°