# Homework Help: Wave Effects of Light

1. May 30, 2005

### koko

I have a test tomorrow and I'm stuck on what to do with this question. If someone could help me I would greatly appreciate it. I'm completely lost on this:

A thin layer of glass (n = 1.50) floats on a transparent liquid (n = 1.35). The glass is illuminated from above by light with a wavelength, in air, of 5.80 x 10^2 nm. Calculate the minimum thickness of the glass, in nanometres, other then zero, capable of producing destructive interference in the reflected light.

2. May 30, 2005

### Staff: Mentor

Compare the light reflected from the first surface (air-glass) with light reflected from the second surface (glass-liquid). For these reflections to destructively interfere, what must their phase difference be?

Two factors contribute to the phase difference. First, is the phase change upon reflection: When light reflects off a surface of higher index of refraction, the reflected wave is phase-shifted by 180 degrees. So there is a phase shift at the first surface, but not at the second. So, if the glass were zero thickness, the two reflections would be 180 degrees out of phase.

The other contribution is due to the second reflection passing through the layer of glass. What phase difference must this contribute to give destructive interference? What thickness (in terms of wavelengths) must the glass be to give that phase difference? Hints: The light passes through the glass twice. What is the wavelength of the light in glass?