Question

The angular width of the central maximum in a single sit diffraction pattern is ${60}^{\circ }.$ The width of the slit is $1\mu m$. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance $50cm$ from the silts. If the observed fringe width is $1cm,$ what is slit separation distance? (i.e. distance between the centres of each slit)

• A. $75\mu m$
• B. $100\mu m$
• C. $25\mu m$
• D. $50\mu m$

Answer 1

The correct option is C $25\mu m$

$\sin {30}^{\circ }=\frac{\lambda }{b}$
$\Rightarrow \lambda =\frac{b}{2}=\frac{1\times {10}^{-6}}{2}=5\times {10}^{-7}m$

Fringe width, $\omega =\frac{\lambda D}{d}$
$\Rightarrow d=\frac{\lambda D}{\omega }$
$=\frac{5\times {10}^{-7}\times 0.5}{1\times {10}^{-2}}$

$d=25\mu m$