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Interference of light

Two glass plates 10cm long are in contact at one end and seperated at the other end by a thread .050 mm in diameter. Light containing two wavelengths 400nm and 600nm is incident perpendicularly. At what distance from the contact point is the next dark fringe?

Please show me the method step by step.
Answer 1.2mm

Solution Preview

The diagram is in the attached file.

From geometry
or x= d l /s------------- Equation (1)
where x is the position of dark fringe

The condition for destructive interference is 2d= m lambda where m=0,1,2

First dark fringe will be for m=0
or 2d=0 or d=0 that is at the contact point
The second dark fringe will be at m=1 or 2d=lambda
or d= lambda /2
The third dark fringe will be ...

Solution Summary

The solution answers a question on interference of light- distance to the next dark fringe.