Coherent sources and their importance in interference

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Question

Two slits are separated by 0.3 mm. A beam of 500 nm light strikes the slits producing an interference pattern. The number of maximas observed in the angular range $- 30 ° < θ < 30 °$ are $590 + p$ . Calculate p = ?

Moderate

Solution

$d \sin θ = n λ$
$\Rightarrow n = \frac{d \sin θ}{λ} = \frac{0.3 \times 10^{- 3} x 0.5}{500 \times 10^{- 9}} = 300$
excluding central maximum 300-1 =299 on each side
Total maximas
299 + 299 + 1 = 599 =590 $+ p$ $\Rightarrow p = 9$

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In an interference arrangement, similar to Young’s double slit experiment, the slits S₁ and S₂ are illuminated with coherent microwave sources, each of frequency 106 Hz. The sources are synchronized to have zero phase difference. The slits are separated by distance d = 150.0 m. The intensity $I_{(θ)}$ is measured as a function of $θ$ , where $θ$ is defined as shown in the figure. If I₀ is maximum intensity, then $I_{(θ)}$ for
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