A beam of unpolarized sunlight strikes the vertical plastic wall of a water tank

Question

A beam of unpolarized sunlight strikes the vertical plastic wall of a water tank at an unknown angle. Some of the light reflects from the wall and enters the water (figure below). The refractive index of the plastic wall is 1.59.   If the light that has been reflected from the wall into the water is observed to be completely polarized, what angle does this beam make with the normal inside the water?

A beam of unpolarized sunlight strikes the vertical plastic wall of a water tank at an unknown angle. Some of the light reflects from the wall and enters the water (figure below). The refractive index of the plastic wall is 1.59. If the light that has been reflected from the wall into the water is observed to be completely polarized, what angle does this beam make with the normal inside the water?

Explanation / Answer

Brewster's Law states that when unpolarized light strikes an interface the reflected light is completely polarized perpendicular to the surface if the incidence angle = the polarizing angle

or ?p = arctan(nb/na) = arctan(1.59/1.333) =50.02

But you asked for the refracted angle in the water

So 1.59*sin(50.02) = 1.333*sin(?)

or ? = arcsin(1.59*sin(50.02)/1.333) = 66.06 deg

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