thin layer question

[crazyasian]

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BR p 243 example 10.9a says" A thin layer of plastic (N=1.46) coats the surface of a glass plate (N=1.52). when monochromatic light is shined normally onto the plastic from the air above, constructive interference occurs. Destructive interference will occur when the coated glass is immersed in which of the following liquids?

I. Water (N=1.33)
II. Carbon Tetrachloride (N=1.46)
III. benzene (n=1.50)

So basically you get a 180 shift every time you go from a lower index of refraction to higher. The answer says benzene is the correct answer, but i thought the answer should be water. Can someone explain this to me? Isn't an even number of phase shifts constructive and odd number of phase shifts destructive?

 

[Salient]

Seems like a ******ed question to me, since the type and strength of interference also has to do with the thickness of the material. Ignoring that simplifies it to the point of abject uselessness 🙁

But if you just look at their example:

originally you have
Air to Plastic to Glass (two 180 shifts)
Benzene to Pastic to Glass (one 180 shift)

You don't consider air to benzene, you are replacing air with benzene. You can't use water because since we don't consider the air to water barrier, you still have two 180 shifts.

 

[crazyasian]

ok that makes sense. I kept adding in benzene and water as another barrier, didn't think that it would replace air. Its so obvious now. Thank you.