Curved glass and Newton's Rings

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A piece of curved glass with a radius of 10m is used to create Newton's Rings, resulting in 100 dark fringes, with the last one at the outer edge. The wavelength of the light used is 654 nm. The problem requires calculating the radius of the outermost dark ring, using the assumption that the radius is much larger than the ring radius. The hint suggests using small angle approximations where tan(theta) equals theta in radians. The discussion highlights confusion regarding the appropriate equations to apply, particularly distinguishing between Newton's Rings and single slit diffraction.
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Homework Statement


A piece of curved glass has a radius of r=10m and is used to form Newton's Rings. Not counting the dark spot in the center of the pattern, there are one hundred dark fringes the last one on the outer edge of the curved piece of glass. The light being used has a wavelength of 654 nm in a vacuum. What is radius R of the outermost dark ring in the pattern?

Hint:r >> R you may assume Tan(theta)= theta for small angles, where theta must be expressed in radians.
lamda = 654 E-9 m= 100

Homework Equations



the only equation that I can find that is even close is Sin(theta)= m* lamda/ W that is use for single slit diffraction. I really do not know how to set this up. The hint is no help to me at all.
 
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I believe the following page should aid you.

http://www.fas.harvard.edu/~scdiroff/lds/LightOptics/NewtonsRings/NewtonsRings.html
 

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