# In a single slit experiment a wave of wavelength $0.2 \;cm$ is incident normally on a slit of width $0.004\;m$ . What is the semi angular width of the central maxima.

$(a)\;60^{\circ} \\ (b)\;30^{\circ} \\ (c)\;15^{\circ} \\ (d)\;0^{\circ}$

For diffraction,
For central maxima
$a \sin \theta =\lambda$
$\sin \theta =\large\frac{\lambda}{a}$
$\theta= \sin ^{-1} \bigg( \large\frac{\lambda}{a}\bigg)$
here $\lambda = 2\times 10^{-3}$
$a= 0.04 m$
$\quad= 4 \times 10^{-3}\;m$
$\theta =\sin ^{-1} \large\frac{1}{2}$
$\qquad= 30^{\circ}$
Hence b is the correct answer.