Two identical light waves having phase difference `'phi'` propagate in same direction. When they superpose, the intensity of resultant wave is proportional to

Options

A. `cos^(2)phi`
B. `"cos"^(2)(phi)/(2)`
C. `"cos"^(2)(phi)/(3)`
D. `"cos"^(2)(phi)/(4)`

Answer

B

Explanation

for two light waves of intensities `I_(1) and I_(2)` and phase difference `phi`, the resultant intensity,
`I_(R)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi`
If the waves are identical, then `I_(1)=I_(2)=I`, then
`I_(R)=I+I+2Icosphi=2I(1+cosphi)`
`=2Ixx2"cos"^(2)(phi)/(2)=4I"cos"^(2)((phi)/(2))`
`therefore I_(R)="cos"^(2)((phi)/(2))`.