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Question
Using analytical method for interference bands, obtain an expression for path difference between two light waves.
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Solution
a) Let S1 and S2 be the two coherent monochromatic sources which are separated by short distance d. They emit light waves of wavelength λ
b) Let D = horizontal distance between screen and source
c) Draw S1M and S2N ⊥ AB
OP = perpendicular bisector of slit.
Since S1P = S2P, the path difference between waves reaching P from S1 and S2 is zero, therefore there is a bright point at P.
d) Consider a point Q on the screen which is at a distance x from the central point P on the screen. Light waves from S1 and S2 reach at Q simultaneously by covering path S1Q and S2Q, where they superimpose
h). If x << D and d << D then,
S1Q ≈ S2Q ≈ D
S2Q + S1Q = 2D
∴ Equation (3) becomes,
`S_2Q - S_1Q = (2xd)/(2D)`
`:. S_2Q - S_1Q = (xd)/D`
`:.trianglex = (xd)/D` .........4
Equation (4) gives the path difference of two interfering light waves
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