Question

Two sources of intensity `I` and 4I are used in an interference experiment. Find the intensity at a point where the waves from two sources superimpose with a phase difference of (a) zero, (b) `pi//2`, (c ) `pi` and (d) ratio of maximum and minimum intensity.

Answer 1

`I_(1)=I, I_(2)=4I`
`I_(R)=I_(1)+I_(2)+2sqrt(I_(1)I_(2)) cos phi`
(a) `phi=0, I_(R)=I+4I+2sqrt(I.4I) cos 0=9I=I_(max)`
(b) `phi=pi/2, I_(R)=I+4I+2sqrt(I.4I) cos(pi//2)=5 I`
(c ) `phi=pi, I_(R)=I+4I+2sqrt(I.4I) cos(pi)=I=I_(min)`
(d) `I_(max)/I_(min)=(9I)/I=9`
OR
`I_(max)/I_(min)= ((sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))-sqrt(I_(2))))^(2)=((sqrt(I)+sqrt(4I))/(sqrt(I)-sqrt(4I)))^(2)=9`