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## Homework Statement

Light strikes two plane sheets of glass with a thin air space between them as shown. If the light has a wavelength of 580 nm and the air space between the glass has a thickness of 870 nm, predict whether the reflected light as demonstrated by rays A and B will cancel or produce a bright spot.

## Homework Equations

2t=mλ, m=1,2,3...

## The Attempt at a Solution

So using the above equation, and substituting the values in the question, I obtain, m=3. So the path difference is 3λ (extra distance ray B travels)

Then since the second ray (ray B) is reflected from a denser medium (glass), it is in phase reversal or λ/2 out of phase. So, then the total path difference is 3.5 λ. Since its a half-integral multiple it implies the rays will cancel-produce a dark spot.

Is this logic correct?

I've been told this is the correct answer, but initially I would have said that the path difference is 3λ, since the rays are already out of phase-and destructive interference would occur-producing a dark spot. Then the whole integral number of wavelengths (3λ in this case), wouldn't change the status of the system, so the rays will cancel. But this is supposedly wrong, with the first answer being correct.

Can someone please clarify why this is true.