Two coherent sources of intensities `I_1` and `I_2` produce an interference pattern. The maximum intensity in the interference pattern will be

Options

A. `l_(1)+l_(2)`
B. `l_(1)^(2)+l_(2)^(2)`
C. `(l_(1)+l_(2))^(2)`
D. `(sqrt(l_(1))+sqrt(l_(2)))^(2)`

Answer

D

Explanation

Resultant intensity for two interfering waves is given by
`I_(R)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi`
For maximum `cos phi` = maximum =1
i.e., `phi=0,pm2pi,pm4pi`
or `phi=pm2pin, n=0,1,2...`
`I_(max)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))`
`=(sqrt(I_(1))+sqrt(I_(2)))^(2)`