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Question

A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. Use D=1.2 m and d=2 mm.

A) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.

B) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

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Solution

A) Given,
n = 3
λ=650 nm
D=1.2 m
d=2 mm
Distance of nth bright fringe from central maxima:
Y=nλDd
Y=3×1.2×103×650×1062
Y=1.17mm
Final Answer : 1.17mm.

B) Given,
λ=650 nm
D=1.2 m
d=2mm
Distance of nth bright fringe from central maxima:
Y=nλDd
Yλ

At a distance Y, nth bright fringe of 520 nm coincides with (n1)th bright fringe of 650 nm,
Ynth=Yn1th
nλ1Dd=(n1)λ2Dd
nλ1=(n1)λ2
Putting values
520 n=(n1)650
n=5
Distance Y from central maxima,
Y=5×520×106×1.2×1032
Y=1.56 mm
Final Answer: 1.56 mm.

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