Interference and Diffraction: Coating on a Lens to Minimize Reflection

[OsDaJu]

Homework Statement

What is the minimum thickness of coating which should be placed on a lens in order to minimize reflection of 661 nm light? The index of refraction of the coating material is 1.40 and the index of the glass is 1.65.

Hint: You must take into account the 180 degree phase-jump on reflection of light from a medium with a lower index of refraction to a medium of higher index of refraction. Also remember that the wavelength of light changes in a medium. The antireflective coating should be half of the minimum length you determine is necessary for destructive interference to occur.

Homework Equations

Dsin(theta)=m*lambda

The Attempt at a Solution

I don't know how to approach this problem. I have read http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/antiref.html#c3 but I don't see it. Can anyone help me?

 

[mgb_phys]

You are trying to find the thickness where light reflected off the front surface and light traveling through the coating and reflecting from the rear surface are out of phase - they then interfere destructively and cancel, giving no reflection.

 

[OsDaJu]

That's what I think I have been asked to find, however I cannot come up with an equation. Do you have any other hints? I would like to understand the problem better. Thank you for the quick reply!

 

[mgb_phys]

It's really just a matter of drawing the diagram - you need a whole number of half wavelengths in the thickness of the layer.
Remember that you have two trips through the layer, the 'distance' inside the layer is effected by the refractive index, and you have to be careful about phase changes at the edge