The Polarizing Rain Gauge · AI Generator #GEN-2AAC84A4
Physics · optics
Problem
A meteorologist designs a clever rain gauge using polarization optics. The device consists of a transparent acrylic cylinder (refractive index n=1.49) partially filled with water. A laser beam enters the cylinder horizontally at the air-acrylic interface. When the beam hits the water surface inside the cylinder, it undergoes total internal reflection if the water level is below a critical height.
The laser is unpolarized initially, but the meteorologist places a polarizer before the cylinder that transmits only light polarized in the plane of incidence (p-polarized). She notices that when the laser beam hits the air-water interface at exactly Brewster's angle, the reflected beam completely disappears.
(a) At what angle θB (measured from the normal to the water surface) does the incident beam hit the water surface when Brewster's condition is satisfied?
(b) If the horizontal laser beam enters the acrylic cylinder at height h=12.0cm above the bottom, what is the water depth d when Brewster's angle condition is achieved at the air-water interface?
Given: The acrylic cylinder has inner radius R=8.0cm, and the refractive index of water is nw=1.33.