In an interference arrangement similar to Young’s double-slit experiment, the slits $S_{1}$ and $S_{2}$ are illuminated with coherent microwave sources, each of frequency $10^{6}$ Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance $d = 150.0 m .$ The intensity $I (θ)$ is measured as a function $θ$ , where $θ$ is defined as shown. If $I_{0}$ is the maximum intensity, then $I (θ)$ for $0 \leq θ \leq 90^{0}$ is given by:

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$I (θ)$ is constant for all values of $θ$

$I (θ) = I_{0} / 4 f o r θ = 90^{0}$

$I (θ) = I_{0} / 2 f o r θ = 30^{0}$

$I (θ) = I_{0} f o r θ = 0^{0}$

answer is A, C.

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Detailed Solution

$λ = \frac{C}{ν} = \frac{3 \times 10^{8}}{10^{6}} = 300 m Δ x = d \sin θ θ = 90^{0} \Rightarrow Δ x = d Δ ϕ = \frac{2 π}{λ} . d = \frac{2 π}{300} \times 150 = π I = I_{0} \cos^{2} (\frac{π}{2}) = 0 Δ x = d \sin 30 = \frac{d}{2} Δ ϕ = \frac{2 π}{λ} . \frac{d}{2} = \frac{π}{300} \times 150 = \frac{π}{2} I = I_{0} \cos^{2} (\frac{Δ ϕ}{2}) = \frac{I_{0}}{2} \begin{array}{l} θ = 0^{0}, Δ x = d \sin θ = 0 \\ Δ ϕ = 0 \\ I = I_{0} \end{array}$