Four monochromatic and coherent sources of light emitting waves in phase at placed on y axis at y = 0, a, 2a and 3a. If the intensity of wave reaching at point P far away on y axis from each of the source is almost the same and equal to `I_(0)`, then the resultant intensity at P for `a=(lambda)/(8)` is `nI_(0)`. The value of `[n]` is.
Here [] is greatest integer funciton.

Answer

`06.00`

Explanation

`lamda = lamda/8`
`phi` between 1 and 3 `=(2pi)/lamdaxxlamda/4 =pi/2`
`phi` between 2 and 4 `=pi/2`
Intensity because of 1 and 3, 2 and 4
`= I_1 +I_2 +2sqrt(I_1I_2)cos phi= I_0+I_0 +2sqrt(I_0I_0)cos (pi//2)= 2I_0`
Now phase difference between resultant of 1 and 3, 2 and 4 `pi/4`
`:. I=I_1+I_2+2sqrt(I_1),sqrt(I_2) cos d `
`= 2I_0+2I_0+2sqrt2 xxsqrt2I_0 xx1/sqrt2`
`4I_0 + 2 sqrt2I_0`
`(4I_0 +2sqrt2)I_0`
`= 6.8 I_0`
`:. [n] = 6`