Monochromatic light waves of intensities `I_(1) and I_(2)`, and a constant phase difference `phi` produce an interference pattern. State an expression for the resultant intensity at a point in the pattern. Hence deduce the expressions for the resultant intensity, maximum intensity and minimum intensity if `I_(1)=I_(2)=I_(0).`

Explanation

Consider a two-source interference pattern produced by monochromatic light waves of intensities `I_(1) and I_(2),` and a constant phase difference `phi`. The resultant intensity at a point in the pattern is
`I=I_(1)+I_(2)+2 sqrt(I_(1)*I_(2))*cos phi " " ` ...(1)
If `I_(1)=I_(2)=I_(0),`
`I=I_(0)+I_(0)+ 2 sqrt(I_(0) * I_(0))* cos phi `
`=2I_(0)(1+cos phi) " " ` ...(2)
At a point of constructive interference with maximum intensity, `cos phi =1` and
`I_(max) =2I_(0)(1+1)=4I_(0) " " `...(3)
At a point of destructive interference with minimum intensity, `cos phi = -1` and
`I_(min) =2I_(0) (1-1)=0 " " `...(4)