Question

Derive an expression for Resultant intensity in YDSE if
the intensity through each slit is same

Answer 1

Answer:

Solution

Let y1 and y2 be displacement of two waves having same amplitude a and phase difference ϕ between them.

y1=asinωt

y2=asin(ωt+ϕ)

Resultant displacement is: y=y1+y2

y=asinωt+asin(ωt+ϕ)=asinωt(1+cosϕ)+cosωt(asinϕ)

Rcosθ=a(1+cosϕ)

Rsinθ=asinϕ

y=Rsin(ωt+θ)

Where, R is resultant amplitude at P, I is intensity, squaring the equations we get,

I=R2=a2(1+cosϕ)2+a2(sinϕ)2=2a2(1+cosϕ)=4a2cos22ϕ

Maximum intensity

cos22ϕ=0

ϕ=(2n+1)π where n=0,1,2,3,....