Light from two coherent sources of the same amplitude A and wavelength `lambda` illuminates the screen. The intensity of the central maximum is `I_(0)`. If the sources were incoherent, the intensity at the same point will be

Options

A. `I_(0)/2`
B. `I_(0)`
C. `2I_(0)`
D. `4I_(0)`

Answer

A

Explanation

When the souces are coherent, the resultant intensity at a point on the screenn is calculated by using the relation
`I_(R)=I_(1)+I_(1)+2sqrt(I_(1)I_(2))cosphi`
For the central maximum, `I_(R)=I_(0)`
For coherent sources `phi=0,cosphi=1 and I_(1)=I_(2)=I`
`therefore I_(0)=I+I+2I cos 0^(@)=4I`
(They have same amplitude and intensity)
`therefore I_(R)=2I=(4I)/(2)=(I_(0))/(2)`