First slide

Coherent sources and their importance in interference

Question

Two coherent sources S₁ and S₂ are separated by a distance four times the wavelength $λ$ of the source. The sources lie along y axis whereas a detector moves along + x axis. Leaving the origin and far off points the number of points where maxima are observed is

Moderate

A

2
B

3
C

4
D

5

Solution

$F r o m Δ S_{1} S_{2} D, {(S_{1} D)}^{2} = {(S_{1} S_{2})}^{2} + {(S_{2} D)}^{2} \Rightarrow {(S_{1} P + P D)}^{2} = {(S_{1} S_{2})}^{2} + {(S_{2} D)}^{2} H e r e S_{1} P i s t h e p a t h d i f f e r e n c e = n λ [f o r m a x i m u m i n t e n s i t y] ∴ {(n λ + x_{n})}^{2} = {(4 λ)}^{2} + {(x_{n})}^{2} o r x_{n} = \frac{16 λ^{2} - n^{2} λ^{2}}{2 n λ} T h e n, x_{1} = \frac{16 λ^{2} - λ^{2}}{2 λ} = 7.5 λ x_{2} = \frac{16 λ^{2} - 4 λ^{2}}{4 λ} = 3 λ x_{3} = \frac{16 λ^{2} - 9 λ^{2}}{6 λ} = \frac{7}{6} λ x_{4} = 0 H e n c e, N u m b e r o f p o i n t s f o r m a x i m a b e c o m e s 3$

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