Physics

Problem

The table below lists four surfaces, each characterized by an average root-mean-square (rms) height variation

h_\text{rms}

measured over length scales comparable to the wavelength range

400\,\text{nm} \le \lambda \le 700\,\text{nm}

of visible light.

Surface	$h_\text{rms}$
A. Polished steel	$10\,\text{nm}$
B. Sand-blasted aluminum	$300\,\text{nm}$
C. Frosted bathroom glass	$800\,\text{nm}$
D. Fresh snow surface	$2000\,\text{nm}$

Assume observations are made with white light incident at

45^\circ

to the mean plane of each surface. (a) For each surface, classify whether the dominant reflection of visible light is expected to be primarily specular, primarily diffuse, or a mixture of both. Provide a brief justification for each classification based on the information given. (b) Rank the four surfaces from brightest to dimmest when viewed from the specular reflection direction. Explain the reasoning behind your ranking. (c) Describe how the appearance of Surface C (frosted glass) would change if the illumination were switched to monochromatic near-infrared light of wavelength

1.0\,\mu\text{m}

while all other conditions remain the same. Justify your answer in terms of the roughness-to-wavelength ratio.

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