Question

In Young's experiment, the wavelength of monochromatic light used is 6000 $\stackrel{\text{o}}{\text{A}}$. 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 0.0015 mm. How many bright and dark bands are observed between the two points P and Q?

Answer 1

For Point P,

$S_{2}P-S_{1}P=(2n-1)\frac{\lambda }{2}\Rightarrow 0.0075\times {10}^{-3}=\frac{(2n-1)}{2}6\times {10}^{-7}\Rightarrow n=13$

i.e, ${13}^{th}$ band will occur at P.

$\therefore 12$ bright bands between P and centrer bright band

For point Q

$S_{2}Q-S_{1}Q=(2n-1)\frac{\lambda }{2}0.0015\times {10}^{-3}=\frac{(2n-1)}{2}6\times {10}^{-7}\Rightarrow n=3$

i.e, $3^{th}$ dark band at Q

$\therefore$ No. of bright bands betwween Q and central bright fringe $=2$

$\therefore$ Total bright bands between P and Q

12+2+1 (Central bright band)

$\Rightarrow 15$