Question

In the figure the intensity of waves arriving at D from two coherent sources `S_1` and `S_2` is `I_0` The wavelength of the wave is `lamda=4m`. Resultant intensity at D will be:
A. `4I_0`
B. `I_0`
C. `2I_0`
D. zero

Answer 1

Correct Answer - C
Path differences, `Delta x=S_2D-S_1D=5-4=1m`
The corresponding phase difference will be
`phi=(2pi)/(lamda)Delta x=(2pi)/(4)`,`1=(pi)/(2)`
Using `I=I_1+I_2+sqrt(I_1I_2)cosphi`.
`I=I_0+I_0+2sqrt(I_0I_0)cos(pi)/(2)=2I_0`