Question A bucket of water has a flat, frozen surface of ice (n = 1.31) with a t

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Question

A bucket of water has a flat, frozen surface of ice (n = 1.31) with a thickness of 1.300 micrometers. The liquid is a depth of 2.0 m. (a) Calculate the time it takes light to start at the surface of the ice, travel straight through the ice, reflect off the interface between the ice and the water, and return to the surface of the ice. (b) Calculate the wavelength or wavelengths of visible light that follow a path described in part (a) that will interfere constructively with light that merely reflects off the surface of the ice. (c) Calculate the wavelength or wavelengths of visible light that follow a path described in part (a) that will interfere destructively with light that merely reflects off the surface of the ice.

Explanation / Answer

a) We know that the speed of light in the ice is Vice=c/nice=3e8m/s/1.31=2.29e8m/s.

Assuming a straight (vertical) trayectory, we also know that the two-way time of reflection (i.e. the total travel time from the top surface of the ice to the bottom of the ice sheet) is T=2*thicknessice/Vice=2*1.3e-6m/2.29e8m/s = 1.14e-14 seconds.

b) Since nwater>nice, the condition for constructive interference is:

2d=mlambda/nice (constructive)

2*1.3e-6*1.31=m*lambda=3.406e-6m=3406 nm

Since the visible espectrum of light is constrained to [380, 750] nm

Therefore the wavelength or wavelengths of visible light that follow a path described in part (a) that will interfere constructively are:

for m=5, lambda=681.2 nm

for m=6, lambda=567.66 nm

for m=7, lambda=486.57 nm

for m=8, lambda=425.75 nm

c) We do the same here, but instead we use the destructive interference condition:

2d=(m+0.5)lambda....(m+0.5) * lambda = 3406 nm

for m=5, lambda = 619.27 nm

for m=6, lambda= 524nm

form m=7, lambda=454.13nm

for m=8, lambda=400.7nm

for m=9, lambda=358.53nm

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