Question

Find the half angular width (in degrees) of the central bright maximum in the Fraunhofer diffraction pattern of a slit of width $12\times {10}^{-5}\text{cm}$ when the slit is illuminated by monochromatic light of wavelength $6000\mathring{A}$(integer only)

Answer 1

Given, $a=12\times {10}^{-5}\text{cm};\lambda =6000\mathring{A}$

The half angular width of the central maximum is given by,

$\sin \theta =\frac{\lambda }{a}[\text{provided}\theta =\text{is small}]$

$\therefore \sin \theta =\frac{\lambda }{a}=\frac{6\times {10}^{-5}}{12\times {10}^{-5}}=0.50\Rightarrow \theta ={30}^{\circ }$