Intensity of Interference Pattern
net effect at point P is the superposition of two waves
E(r,t) = Emsin(kr1-?t) + Emsin(kr2- ?t) =>same wavelength and frequency but travel different distances r1 and r2= r1+ ?L
E(r,t) = Emsin(kr1- ?t) + Emsin[k(r1+ ?L)- ?t]
= Em[sin(kr1- ?t) + sin(kr1- ?t+ ?)]
where ?=k ?L is phase shift due to path difference!
sin(A)+sin(B) = 2 cos[(A-B)/2]sin[(A+B)/2]
E(r,t) = 2Emcos(?) sin(kr1- ?t+ ?) ; ?= ?/2