Question

In Young's double slit experiment, the two slits $0.15$mm apart are illuminated by monochromatic light of wavelength $450$nm. The screen is $1.0$m away from the slits. (a) Find the distance of the second. (I) bright fringe, (ii) dark fringe from the central maximum, (b) How will the fringe pattern change if the screen is moved away from the slits?

Answer 1

$a\left)1\right)y=\frac{n\lambda D}{d}=2\times \frac{450\times {10}^{-9}}{0.15\times {10}^{-3}}\times 1=6\times {10}^{-3}m=6mm2)y=(2n-1)\frac{\lambda D}{2d}=(2\times 2-1)\times \frac{450\times {10}^{-9}\times 1}{2\times 0.15\times {10}^{-3}}=4.5mm$

$b)$ as D increases, fringe width $\beta$ as $\beta \propto D$

Best angular separation$(=\frac{\pi }{d})$ remains constant.