Question

Derive an expression for the intensity at any point on the observation screen in youngs double slit experiment

Answer 1

we know, intensity of wave depends on amplitude of wave. e.g., intensity of wave is directly proportional to square of amplitude of wave.

mathematically, I = KA², where K is proportionality constant, I is intensity and A is amplitude.

if two waves, $y_1=A_1sin\omega t$

and $y_2=A_2sin(\omega t+\delta)$

resultant amplitute, $A=\sqrt{A_1^2+A_2^2+2A_1A_2cos\delta}$

so, $A^2=A_1^2+A_2^2+2A_1A_2cos\delta$

or, $\boxed{\bf{I=I_1+I_2+2\sqrt{I_1I_2}cos\delta}}$

this is the expression for the intensity at any point on the observation screen in Young's Double slit experiment.