Derive the expression for the intensity at a point where interference of light occurs. Arrive at the conditions for the maximum and zero intensity.
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Updated on : 2022-09-05
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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=1 ϕ=2nπ where n=0,1,2,3,....
Minmum intensity: cos22ϕ=0 ϕ=(2n+1)π where n=0,1,2,3,....