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Question
Using analytical method for interference bands, obtain an expression for path difference between two light waves.
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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