In Young's double-slit experiment, the two slits act as coherent sources of equal amplitude `A` and of wavelength `lamda`. In another experiment with the same set-up the two slits are sources of equal amplitude `A ` and wavelength `lamda`, but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that in the second case is....

Options

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

Answer

B

Explanation

With two coherent sources, `I_(1)=I_(2)=I_(0)` and at the centre of the screen, `I=4I_(0)`
but with two non-coherent sources, `I_(NC)=I_(1)+I_(2)=2I_(0)`
since the value of cos`phi` I the expression
`I_(R)=I_(1)+I_(2)+2sqrt(I_(1)I_(2)) cosphi`, is zero.
`therefore (I_(Cn))/(I_(NC))=(4I_(0))/(2I_(0))=2`