Question

What are the three smallest non-zero thicknesses of soapy water (n=1.33) on Plexiglas if it appears green (constructively reflecting 520-nm light) when illuminated perpendicularly by white light? Explicitly show how you follow the steps in Problem Solving Strategies for Wave Optics.

a) 123 nm, 246 nm, 369 nm
b) 185 nm, 370 nm, 555 nm
c) 210 nm, 420 nm, 630 nm
d) 275 nm, 550 nm, 825 nm

Answer 1

The three smallest non-zero thicknesses of soapy water on Plexiglas that appear green when illuminated perpendicularly by white light are 195 nm, 390 nm, and 585 nm. None of the option is correct.

Step-by-step explanation:

According to the problem solving strategies for wave optics, we can determine the thickness of the soapy water layer by using the formula for constructive interference:

2nt = mλ

where t is the thickness of the layer, n is the refractive index of the soapy water, m is the order of the interference, and λ is the wavelength of the light.

In this case, we are looking for the thicknesses that produce constructive interference for green light with a wavelength of 520 nm:

2(1.33)t = λ

t = λ / (2n)

Plugging in the values, we get:

t = 520 nm / (2 * 1.33) = 195 nm

The three smallest non-zero thicknesses that appear green are:

195 nm, 390 nm, 585 nm