# Homework Help: Waves: Superposition - Thickness of a Reflective coating

1. Jun 22, 2009

### Prophet029

1. The problem statement, all variables and given/known data

What is the thinnest film of MgF2 (n=1.21) on glass that produces a strong reflection for the light with a wavelength of 531 nm?

2. Relevant equations

Open-Closed Standing wave

Fn= (nv/4L)
v = Wave Length * F

3. The attempt at a solution

Basically, I tried to plug in the data. I solved for Frequency by using velocity for light (300,000,000 m/s) = (5.31*10^-7m) * F
Then used the equation Fn= (nv/4L)
using n = 1.21
Alternatively the eq can be simplified into

L= ((n*wave length)/4)
I get 1.606*10^-7m, but I get the problem wrong. I think I overlooked something, but I'm not sure, can any one help out. Most appreciated.

2. Jun 22, 2009

### Staff: Mentor

This is not what you need. Instead, think about the two reflections that must constructively interfere. What must twice the thickness of the film--the extra distance traveled by one of the reflections--be in terms of wavelengths?

Last edited: Jun 22, 2009
3. Jun 22, 2009

### Prophet029

Ok, I see. If I remember correctly, then 2 waves that constructively interfere have Amplitudes that add up to the Resultant wave amplitudes. But I'm having trouble relating this to the wavelengths. Pardon my lack of knowledge with interfering waves, my lecturer skipped over it and only talked about it briefly. So thank you very much for helping out.

4. Jun 22, 2009

### Staff: Mentor

Reading this discussion might help: http://www.physicsclassroom.com/Class/light/u12l1c.cfm" [Broken]

The key is that the wave that reflects from the bottom surface must end up exactly in phase with the wave that reflects from the top surface in order for them to constructively interfere. So that extra distance--which is twice the film thickness--must equal how many wavelengths?

And how do you calculate the wavelength of light in a medium with refractive index n?

Another discussion that you might find useful is this: http://hyperphysics.phy-astr.gsu.edu/Hbase/phyopt/thinfilm.html#c1"

Last edited by a moderator: May 4, 2017