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A circular oil slick on a calm lake has a maximum depth (in the center) of $800\text{ nm}$. There is a bright red fringe (due to constructive interference) in the middle where the oil slick is thickest.

How many more circular bright red ($\text{wavelength} = 640 \text{ nm}$) fringes are there before the oil slick thins to a thickness of $100\text{ nm}$?

Note: the index of refraction of air is $1.00$, the index of refraction of oil is $1.47$, and the index of refraction of water is $1.33$.

A

$0$

B

$1$

C

$2$

D

More than $2$.

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