What Is the Minimum Thickness for Constructive Interference in a Thin Film?

[Joza]

A thin film is put on the surface of glass, with indexes of refraction of x and y respectively.

If light, with wavelength L in air, is reflected from the 2 sides of the film, to interfere constructively, what is the minimum thickness required.


The question is stated just like that, so I think it is vague in some parts.

I can't think of a formula to work this out. I know for con. interference, 2t=mL, where m is a whole number. But this isn't enough, and doesn't relate the indexes of r.

Any hints?

 

[weathercheck]

Shouldn't be doing your Homework 3 and half hours before its due.. tut tut

 

[Joza]

Haha. I'd usually do it on Saturday, but with a boozin session going down, it didnt get done.

Besides, I'm a member here ages, so the guys can be great help when needed.

So did you get this one? Hey I helped you with the polarizer one

 

[weathercheck]

Sure i got it......

Nah i think I'm retarded, on 40%..

Still can't get the polarizer one or this one or the last one lol

 

[Joza]

Ah...there would have been a nice a pav pint in it for ya.

Hey, what's your name? Don't tell me your TP...

 

[weathercheck]

Im taking a break, think "Fringes from Different Interfering Wavelengths" may be answerable! If i hit 60 i'll be proud! lol ;)

 

[Joza]

I don't think I'll hit 60 this time...


Damn weekends...;)

 

[Doc Al]

I can't think of a formula to work this out. I know for con. interference, 2t=mL, where m is a whole number. But this isn't enough, and doesn't relate the indexes of r.

Assuming x < y, the phase change on reflection is the same for both reflections so all that matters is the phase difference due to traveling through the film. That equation (2t = mL) will work, but L must be the wavelength in the film. That's where the index of refraction comes in.

If x > y, things will be a bit different. Learn more here: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/thinfilm.html"

 

[Joza]

Yes, x > y.

I understand it when x < y.

Then 2t=L, where L is wavelength in the film. So L would be index of refraction in film times wavelength in air.

But x > y...

 

[Doc Al]

Yes, x > y.

I understand it when x < y.

Then 2t=L, where L is wavelength in the film. So L would be index of refraction in film times wavelength in air.

Not exactly. Is the wavelength shorter or longer in the film?

But x > y...

In that case the second reflection undergoes a different phase shift than the first (actually no phase shift). See that link for details.

 

[Joza]

Sorry, divided by...

So does that mean 2t=L?? Or t=L?

 

[Doc Al]

So does that mean 2t=L?? Or t=L?

When x > y, the condition for constructive interference (and minimum thickness) is 2t = L/2 (where L = wavelength in the film).