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Q.
A slit $4 cm$ wide is irradiated with microwaves of wavelength $2 cm$. What will be angular spread of central maximum, assuming incidence normal to the plane of the slit?
Wave Optics
Solution:
$a=4 cm =4 \times 10^{-2} m$
$\lambda=2 cm =2 \times 10^{-2} m$
Angular spread of central maximum $(2 \theta)$ is
$a \sin \theta=\lambda n$
$\sin \theta=\frac{2 \times 10^{-2}}{4 \times 10^{-2}}$
$\Rightarrow \sin \theta=\frac{1}{2} $
$\Rightarrow \theta=30^{\circ}$
Angular spread $=2 \theta=2 \times 30^{\circ}$
$=60^{\circ}$