Destructive interference in wavelengths question

[StudentofPhysics]

1. A nonreflective coating (n = 1.24) covers the glass (n = 1.52) of a camera lens. Assuming that the coating prevents reflection of yellow-green light (wavelength in vacuum = 564 nm), determine the minimum nonzero thickness that the coating can have.




2. wavelength of the light in the coating = wavelngth of light / n of coating

desructive interference: 2t = (1,2...) wavelngth coating
t=thickness



3. OK the wavelngth of the light through the coating is: 564/1.24 = 454.84

I figured maybe that was all i needed and attempted to find t.

2t=1(454.84)
t= 227.42

this was not correct, so I next proceded to find the wavelength once through the film to the glass:

454.84/1.52 = 299.24 nm

The destructive interference for this is:

2t = (1) 299.24
t= 149.62 nm

This too was incorrect.

I even tried plugging in the original wavelength of 564 nm with the n of glass; 1.52, then solving for t. This gave me:

564/1.52 = 371.05
2t= (1) 371.05
t= 185.53


None of these were correct.

Any thoughts on where am I going wrong?

 

[StudentofPhysics]

I think I've made some progress:

Since there are 2 1/2 wave shifts then the equation should be:

2t + 1 wavelength in film = (1/2) wavelength in film

this gave me an answer of 341.13 nm for t and is still incorrect though.

 

[StudentofPhysics]

Ok nevermind I finally figured it out. I was adding the wave shift across the sides of the formula rather than subtracting it like I should have.

Thanks to those who considered it for me though.