The angular width of the central maximum in a single slit 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 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? <br> (i.e. distance between the centres of each slit.)

Question

( A ) $75 \mu m$
( B ) $50 \mu m$
( C ) $100 \mu m$
( D ) $25 \mu m$