At what angle above the horizon would the sun appear if its reflected light from a lake,viewed at the same time,were completely polarized? (n _water = 1.333) A) 53.12$^{\circ}$ B) 36.88$^{\circ}$ C) 48.75$^{\circ}$ D) 41.25$^{\circ}$ E) 23.52$^{\circ}$

Question

Quizplus · Accepted Answer

When light reflects off a flat surface at a particular angle (known as the Brewster angle), the reflected light becomes completely polarized. The Brewster angle is given by:

θB = tan^-1(n)

where n is the refractive index of the medium the light is reflecting off of. In this case, the medium is water, which has a refractive index of 1.333. Therefore:

θB = tan^-1(1.333) = 53.12°

This is the angle at which light reflecting off the surface of the water will be completely polarized. However, we need to find the angle above the horizon at which the sun would appear if its light were reflected off the water and polarized.

This angle can be found using the relationship between the Brewster angle and the angle of incidence:

θB + θi = 90°

where θi is the angle of incidence (i.e. the angle between the incident light and the surface of the water). Solving for θi:

θi = 90° - θB = 36.88°

Therefore, the answer is B) 36.88°.

At What Angle Above the Horizon Would the Sun Appear ∘^{\circ}∘

At What Angle Above the Horizon Would the Sun Appear $^{\circ}$