Query 15

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course PHY 232

1:09 pm 3/25 pm

`Query 15 PHY 232 

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Question: `q**** query univ phy problem 33.44 11th edition 33.38 (34.28 10th edition) 3 mm plate, n = 1.5, in 3 cm separation between 450 nm source and screen. How many wavelengths are there between the source and the screen?

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Your solution:

I have a couple of problems with this. One is that it doesn't indicate where the glass plate is actually placed. That is how far from the screen and source since the wavelength coming out is different than going in and so the wave isn't the same and unless the plate is on the screen then there will be fewer wavelengths in that part of the air than on the other side. I guess I'll assume that the plate is against the screen so that the wavelength of the light that hits it is the glass wavelength and I'm using the book values as well.

lambda = lambda_0/n = 450 nm/ 1.4 = 386 nm

air distance = 1.8 cm - 2.5 mm = 1.55 cm

1.5*10^7 nm/450 nm = 3.33*10^4

2.5*10^4 nm = 62.2

 

 

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Given Solution:

`a** The separation consists of 1.5 cm = 1.5 * 10^7 nm of air, index of refraction very close to 1, and 1.5 mm = 1.5 * 10^6 nm of glass, index of refraction 1.5.

 

The wavelength in the glass is 450 nm / 1.5 = 300 nm, approx..

 

So there are 1.5 * 10^7 nm / (450 nm/wavelength) = 3.3 * 10^4 wavelengths in the air and 1.5 * 10^6 nm / (300 nm/wavelength) = 5.0 * 10^3 wavelengths in the glass. **

 

STUDENT QUESTION

After reading the solution, I am unsure about why the path difference is equal to twice the plate thickness.
INSTRUCTOR RESPONSE

One ray is reflected from the 'top' surface of the plate. The other passes through the plate to the other surface, is reflected there. It has already passed through the thickness of the plate. It has to pass back through the plate, to the other surface, before it 'rejoins' the original ray. It has therefore traveled an extra distance equal to double that of the plate.

 

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Self-critique (if necessary): The values used in the solution are all messed up so I'm not certain I got this completely right. I noted the part about being twice the thickness of the glass but that seems to be if the light were reflected where here it passes through the glass to the screen. If I understand the setup correctly that is.

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&#Your work looks good. See my notes. Let me know if you have any questions. &#