A laboratory technician compares two stainless-steel plates, Plate X and Plate Y, that are identical in size and composition but differ in microscopic roughness. A laser beam of power P0=10mW strikes the center of each plate at normal incidence.
A detector that subtends a solid angle corresponding to a 10∘ half-angle cone is placed so that its central axis is aligned with the expected specular direction for each plate.
Measurements show that for Plate X the detector receives 1.6mW, whereas for Plate Y it receives 0.064mW.
Assume the fraction of incident power sent into that 10∘ cone is inversely proportional to the square of the plate’s root-mean-square (RMS) roughness r.
Answer the following questions.
(a) Determine the ratio rY/rX of the RMS roughness values for the two plates.
(b) For Plate Y, estimate the fraction of the incident power that is scattered outside the 10∘ cone.
(c) Sketch on qualitatively labeled axes the angular power distribution (power per unit solid angle versus scattering angle) you would expect for each plate. Clearly indicate which curve corresponds to which plate and justify the relative widths of the curves.