The Photographer's Polarizing Filter Mystery · AI Generator #GEN-7BD41F34
Physics · optics
Problem
A wildlife photographer notices something strange while photographing a lake at sunset. When she rotates her circular polarizing filter, the brightness of the reflected sunlight from the water surface varies dramatically, but the brightness of a white bird standing in the shallow water remains nearly constant. She measures the angle of the sun above the horizon to be 37°.
The polarizing filter reduces the intensity of polarized light by a factor that depends on the angle θ between the light's polarization direction and the filter's transmission axis, following I=I0cos2θ.
When the filter is oriented to completely block the reflected sunlight from the water, she measures that the bird appears 3.2 times brighter relative to the (now very dim) reflected background compared to when the filter allows maximum transmission of the reflected light.
What is the refractive index of water? You may assume the reflected sunlight is completely polarized and the bird reflects unpolarized light.