A wall is coated with matte white paint whose microscopic facets are randomly…
PHYSICS · Single correct · AP · Physics 2: Algebra-based · Geometric Optics · Geometric Optics
Problem
A wall is coated with matte white paint whose microscopic facets are randomly oriented within approximately ±10∘ of the macroscopic wall plane. A narrow red laser beam (λ=650nm) strikes the wall at an incidence angle of 50∘ relative to the normal. Two photodetectors are used:
• Detector 1 is positioned at the angle predicted by the law of reflection for a perfectly smooth surface.
• Detector 2 is placed on the original beam axis, just in front of the laser, to measure any light that is reflected back toward the source.
Detector 2 records a measurable intensity, while Detector 1 registers an intensity far below the incident beam’s power. Which of the following statements best accounts for these measurements?
(a) Because the surface roughness is comparable to the laser wavelength, the reflected beam undergoes diffraction; the central diffraction maximum is shifted away from the specular angle and partially back along the incident path, so Detector 1 sees little light while Detector 2 records some.
(b) The incidence angle is close to Brewster’s angle for the paint–air interface, so the component that would reach Detector 1 is suppressed by polarization effects, whereas the reflected component is directed back toward the source and detected by Detector 2.
(c) Because the wall’s microscopic facets are randomly oriented, most reflected rays deviate from the perfect specular direction, greatly reducing intensity at Detector 1 and sending some rays back toward Detector 2.
(d) The red photons are first absorbed by the paint and then spontaneously re-emitted isotropically; very few re-emitted photons travel in the specular direction, but some happen to return toward the laser and are measured by Detector 2.