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Question

Two slits separated by a distance of 1mm are illuminated by light of wavelength 6.5×107m. Interference fringes are oberved on a screen placed at a distance of 1 from the slits. Calculate the distance between the third dark fringe and fifth bright fringe.

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Solution

Given:
Slit separation, d=1mm=1×103m
Wavelength, λ=6.5×107m
Screen distance , D=1m
To find:
Distance between 3rd dark fringe and 5th bright fringe

We know,
For distance of dark fringe, yn=(2n1)λD2d
And, for distance of bright fringe, yn=nλDd
y5y3=5×6.5×107×1103(2×31)×6.5×107×12×103=32.5×10416.25×104=16.25×104m
Hence the distance between the third dark fringe and fifth bright fringe is 1.625mm

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