Understanding Optics: Why is 2t changed to 2tn in problem 35.54?

[Niles]

Homework Statement

Hi all.

Please take a look at page 4 in this PDF, namely problem 35.54: http://faculty.physics.tamu.edu/hu/221-fl08/YF-ch35-exmpls-new.pdf

My questions is: Why is it that the equation $2t = (m+\frac{1}{2})\pi$ is changed to $2tn = (m+\frac{1}{2})\pi$?

I know it is because we are in air now, but the light still travels a distance of 2t, and not 2tn? Can you explain this to me?Thank you very much in advance.Niles.

 

[Doc Al]

The issue is not the distance, but how many wavelengths it corresponds to. The distance in the glass is 2t, so you'd express that as some multiple of wavelengths in the glass. If instead you want your equation in terms of wavelengths in air, then you need to multiply by n. (Since the wavelength decreases by a factor of n when entering the glass.)

 

[Niles]

I am not entirely sure I understand your post. Am I correct when I say that what you wrote is essentially

$$2t = (m+\frac{1}{2})\lambda_{glass}$$

AND$$2tn = (m+\frac{1}{2})\lambda_{air}$$

and this is because we have $n=\lambda_{air}/\lambda_{glass}$ (approximately)?

 

[Doc Al]

Exactly.

 

[Niles]

Thanks. I had a hectic day today, and it means a lot that you responded so swiftly.