 #1
Abu
Homework Statement
A total of 31 bright and 31 dark Newton's rings (not counting the dark spot at the center) are observed when 550nm light falls normally on a planoconvex lens resting on a flat glass surface. How much thicker is the center than the edges?
Homework Equations
2t = mλ
2t = (m+1/2)λ
The Attempt at a Solution
The above image is just one I found online. As for my attempt:
Since the incident ray is being reflected off of a surface where it would have gone faster had it not been reflected, there is no phase shift. However, when it reflects off of the flat glass, it is being reflected off of a surface where it would have gone slower had it not been reflected, thus giving a phase shift.
That means that the formula I will be using is:
2t = mλ for destructive interference
2t = (m+1/2) for constructive interference.
As it is asking how much thicker the center is than the end, my first instinct is to find the thickness of the center, than find the thickness at the very edge, and find the difference.
Since the center is destructive however, the formula used is 2t = mλ
The center means that m = 0
That means that the thickness of the air film between the curved surface is zero (which I think makes sense because there is no room for air at the center)
The furthermost point of the newton rings is destructive interference (NOT SURE ABOUT THIS) because the last ring would have color, and beyond that there is no more color.
So I am tempted to use this formula:
2t = mλ for destructive interference
So...
2t = 31(550)
t = 8525 nm
Can someone tell me if my reasoning is right? Specifically how I assume the furthermost point is destructive interference and also how I assume that the thickness in the center is zero. Also, why does the question say how much thicker is the center than the edges when in reality the center has zero thickness (value for t was zero)
Thank you for your time.
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