Question

Expression for the intensity at any point on the observation screen in young double slit experiment. Hence write the conditions for constructive and destructive interference

Answer 1

Heya Friend,

This was just a complicated issue to types such expressions on the keyboard....

{Please refer the first & second attachment respectively for the answer}

Hope it helps....

#Phenomenal

Answer 2

Answer:

The expression for the intensity at any point  in 'young double slit experiment' $\mathrm{W}=\frac{x 1 \lambda}{x}$

Explanation:

Suppose there are 2 slits namely H1 and H2 that are at a distance of X. A strong monochromatic light of λ wavelength has been focused on the screen containing slits and another screen RS is at a distance X1 from the slits.

Let there be a point P at a distance b from center of screen RS. The difference in path of waves arriving from slits will be H2P-H1P.  

$(\mathrm{H} 2 \mathrm{P})_{\mathrm{ln}}^{2}-(\mathrm{H} 1 \mathrm{P})^{2}=\left(\mathrm{X} 1^{3}+\left(\mathrm{Y}+(\mathrm{b} / 2)^{2}\right)-\left(\mathrm{X} 1^{3}+\left(\mathrm{Y}+(\mathrm{b} / 2)^{2}\right)\right.\right.$

$\mathrm{H} 2 \mathrm{P}-\mathrm{H} 1 \mathrm{P}=\frac{2 b X}{\mathrm{H} 2 \mathrm{P}+\mathrm{H} 1 \mathrm{P}}$

$\mathrm{H} 2 \mathrm{P}+\mathrm{H} 1 \mathrm{P}=2 \mathrm{X} 1$

$\mathrm{H} 2 \mathrm{P}-\mathrm{H} 1 \mathrm{P}=\frac{b X}{X 1}$

For constructive interference where n = 0,1,2,3

$\mathrm{B}=\frac{X 1 \lambda}{X}$

For destructive interference where n=0, 1, 2, 3

$\mathrm{B}^{1}=\frac{X 1 \lambda}{X}$

Difference between bright and dark fringes $\mathrm{W}=\frac{X 1 \lambda}{X}$