In Young's double slit experiment of central fringe is `I_(0)` and fringe width is `beta`. If a point is at a distance x from the central fringe, then the intensity at that point is

Options

A. `l_(0)cos^(2)((pix)/beta)`
B. `l_(0)cos^(2)((x)/beta)`
C. `l_(0)/4cos^(2)((pix)/beta)`
D. `l_(0)cos^(2)((pibeta)/x)`

Answer

A

Explanation

Intensity at distance x from central maximum is given by
`I=4I_(0)"cos"^(2)phi/2`
where, `phi=(2pid)/lamdasintheta`
Also, `beta=(lamdaD)/d`
Combining these, we get
`I_(0)=I_(0)cos^(2)((pix)/beta)`