Coating Eyeglass Lenses(destructive interference)

[Joe Butler]

Homework Statement

Eyeglass lenses can be coated on the inner surfaces to reduce the reflection of stray light to the eye. If the lenses are medium flint glass of refractive index 1.62 and the coating is fluorite of refractive index 1.432, (a) what minimum thickness of film is needed on the lenses to cancel light of wavelength 550nm reflected towards the eye at normal incidence, and (b) will any other wavelengths of visible light be canceled or enhanced in the reflected light?

Homework Equations

2nt = (m+.5)λ
n = refractive index of film
t = thickness of film
m = 1, 2, 3, …
λ = light wavelength in vacuum (air)

The Attempt at a Solution

I have already solved the first part to find that t=96.01nm but i don't know how to solve for part b. I was thinking that you would have to plug the thickness 96.01nm into 2nt = mλ to solve for any possible constructive interference wavelengths but i am not sure.

 

[TSny]

Yes, you are thinking correctly.
From part (a), you now know the thickness t. So it is no longer an unknown.
For part (b), λ is the unknown in the equations 2nt = (m+.5)λ and 2nt = mλ. (You want to investigate both constructive and destructive interference.)