Interference patterns in thin films

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haha1234
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Why the interference patterns are separated when there are many light beams transmit through the film?
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Thanks!
 
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This is the question

An investigator finds a fiber at a crime scene that he wishes to use as evidence against a suspect. He gives the fiber to a technician to test the properties of the fiber. To measure the diameter d of the fiber, the technician places it between two flat glass plates at their ends as in the figure below. When the plates, of length 15.0 cm, are illuminated from above with light of wavelength 610 nm, she observes interference bands separated by 0.555 mm. What is the diameter of the fiber?

I don't know why there are interference patterns separating,and I want to know if destructive interference occurs,how to measure the diameter of the fibre?
 
This is clearly a homework question. It should be in the Homework section at the very top of the index.

You cannot expect a simple answer for this sort of question on PF. You need to demonstrate that you have actually tried for an answer on your own. Say what you have found out so far and what you think about it. We do not spoon feed students. The topics of thin film interference and Newton's Rings will be thrown up in hundreds of hits on Google. Read what Wiki has to say about it and then come back to discuss it.