In Young's double slit experiment, the two slits act as coherent sources of waves of equal amplitude A and wavelength `lambda`. In another experiment with the same arrangement the two slits are made to act as incoherent sources of wave of same amplitude and wavelength. If the intensity at the middle point of the screen in the first case is l, and in the second case is `I_(2)` then the ratio `(I_(1))/(I_(2))` is .......

Options

A. 4
B. 2
C. 1
D. `0.5`

Answer

B

Explanation

For coherent source in
`I_(1)=I_(0)"cos^(2){(k(r_(2)-r_(1)))/(2)},r_(2)=r_(1)`
`:.I_(1)=I_(0)cos^(2){k((0)/(2))}`
`=I_(0)cos^(2)(0)`
`I_(1)=I_(0)`
but `I_(0)=4I` maximum intensity and `I=I_(0) or I_(2)` is the intensity of one source.
For incoherent source,
`I_(2)=I.+I.+2sqrt(I.I) lt cos delta gt `
`=2I.+2I(0)[ :.` one one period `lt cos delta gt=0]`
`I_(2)=2I.`
`:. (I_(1))/(I_(2))=(4I)/(2I)`
`:.(I_(1))/(I_(2))=2`