Question

In Young's experiment, the wavelength of monochromatic light is used is $6000\stackrel{{}_{\circ }}{A}$. The optical path difference between the rays from the two coherent sources at point P on the screen is 0.0075 mm and at a point Q on the screen is 0.0015mm. How many bright and dark bands are observed between the two points P and Q? (points P and Q are on the opposite sides of central bright band).

Answer 1

Given :$\lambda =6000A^0$

:$\Delta 1.5microns$

:$S=0.0075mm$

For dark fringe at P,

$S_{1}P-S_{2}P=\Delta =(2n-1)\lambda /2$

$\Delta =(2n-1)\times \frac{\lambda }{2}$

$1.5=(2n-1)\times \frac{6\times {10}^{-7}}{2}$

$1.5=(2n-1)3\times {10}^{-7}$

$\frac{1.5}{3}\times {10}^7=(2n-1)$

$\frac{1}{2}\times {10}^7=(2n-1)$

$\frac{1}{4}\times {10}^7=n-1$

$0.25\times {10}^7=n-1$

$2.5\times {10}^6=n-1$

$2.5+1\times {10}^6=n$

$3.5\times {10}^6=n$

thus $n=3darkfringes$