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A slit whose width is 5.0 cm is irradiated with microwaves of wavelength 2 cm. The angular spread of the central maxima? (Assume that the incidence is along the normal to the plane of the slit ) is

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${2sin}^{- 1} (2 / 5)$

${sin}^{- 1} (2 / 5)$

${cos}^{- 1} (2 / 5)$

${cos}^{- 1} (4 / 5)$

answer is A.

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Detailed Solution

$Angular spread of central maximum (2 θ) is$

$\begin{array}{l} a \sin θ = λ n \\ \sin θ = \frac{2 \times 10^{- 2}}{5 \times 10^{- 2}} \\ \Rightarrow \sin θ = \frac{2}{5} \end{array}$

Angular width = ${2sin}^{- 1} (2 / 5)$

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