The wavelength of the waves arriving at P from two coherent sources `S_1` and `S_2` is 4m, while intensity of each wave is `I_0`. The resultant intensity at `P` is `2I_0`. Find the minimum value of `S_2P`

Options

A. `(xsqrt5)/(2)`
B. `2x`
C. `(x+1)`
D. `(x+sqrt2)`

Answer

C

Explanation

`I=I_0+I_0+2sqrt(I_0.I_0)cosphi=2I_0`
so `cosphi=0`
`phi=(npi)/(2)=(pi)/(2)`
(`n=1` for `S_2P` to be minimum)
`phi=((2pi)/(lamda)) Delta x=((2pi)/(4)) Delta x(pi)/(2)`
`Delta x=1m`
`Delta x=S_2P-S_1P=1`
`S_2P=S_1P+1=(x+1)` metres
thus the detector should be placed at a distance of 3 m from the source. Note that there is no abrupt phase change.