Explain the theory of interference of light.

Explanation

Let `Y_(1)=asinomegat` and `Y_(2)=bsin(omegat+phi)` be two light waves interfere giving rise to resultant `Y=Y_(1)+Y_(2)`
Net displacement from principle of superposition
`Y=Y_(1)+Y_(2)`
`Y=asinomegat+bsin(omegat+phi)=asinomegat+b(sinomegatcosphi+cosomegatsinphi)`
`=sinomegat(a+bcosphi)+bsinphicosomegat`
Let `a+bcosphi=Rcostheta` and `bsinphi=Rsintheta`
`Y=Rsinomegatcostheta+Rcosomegatsintheta=Rsin(omegat+theta)`
`R=sqrt(a^(2)+b^(2)+2abcostheta)`
OR the wave with equal amplitude must be considered.
`R=sqrt(2a^(2)+2b^(2)+2acostheta)=2acos.(theta)/(2)`