Fringes and Phase in Optics: Solving Problem 35.61

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Niles
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Homework Statement


Hi all

Please take a look at problem 35.61 in this PDF (it is on page 5): http://physics.wustl.edu/classes/SP2009/212/homework/YF35.pdf

What I can do is to find the "extra" phase accumulated in the glass rod per minute. But I do not know how to transform this into a number of fringes?
 
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Ok, I got the answer 22.7, which is also correct. I got it by finding

(phase gained per minute) - (phase gained at T=20 degrees) / 2Pi.

But this was pure luck - I cannot see, why this gives me the correct answer.
 
Guys, I am sorry about doing this, but I really need help with this. This is such a fundamental thing that I must understand it. Can you give me a hand?