The intensity of each of the two slits in Young's double slit experiment is `I_(0)` Calculate the minimum separation between the two points on the screen where intensities are `2I_(0)` and `I_(0)` Given the fringe width equal to `alpha`

Options

A. `alpha/4`
B. `alpha/3`
C. `alpha/12`
D. None of these

Answer

C

Explanation

`2I_(0)=4I_(2)"cos"^(2)phi/2`
`phi=pi/2=(2pi)/lambda.Deltax=(2pi)/lambda.((y_(1)d)/D)`
`:.y_(1)=(lambdaD)/(4d)`
Further `I_(0)=4I_(0)"cos"^(2)phi/2`
`rArrphi=(2pi)/3=(2pi)/lambdaDeltax=(2pi)/lambda((y_(2)d)/D)`
`:.y_(2)=(lambdaD)/(3d)`
Minimum separation `Deltay=y_(2)-y_(1)=1/12((lambdaD)/d)=alpha/12`