Chapter 34, Problem 37P

(II) Let’s explore why only “thin” layers exhibit thin-film interference. Assume a layer of water, sitting atop a flat glass surface, is illuminated from the air above by while light (all wavelengths from 400 nm to 700 nm). Further, assume that the water layers thickness t is much greater than a micron (= 1000 nm); in particular, let t = 200 μm. Take the index of refraction for water to be n = 1.33 for all visible wavelengths. (a) Show that a visible color will be reflected from the water layer if its wavelength is λ = 2nt/m, where m is an integer. (b) Show that the two extremes in wavelengths (400 nm and 700 nm) of the incident light are both reflected from the water layer and determine the m-value associated with each. (c) How many other visible wavelengths, besides λ = 400 nm and 700 nm, are reflected from the “thick” layer of water? (d) How does this explain why such a thick layer does not reflect colorfully, but is white or grey?