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 `beta.`

Options

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

Answer

C

Explanation

`2I_0 = 4I_0 cos^2 (theta_1/2)`
` :. phi_1 = pi/2 = ((2pi)/lambda)(Deltax_1)= ((2pi)/lambda)((y_1d)/D)`
`:. y_1 = (lambdaD)/(4d) = beta/4`
Further, `I_0 = 4I_0cos^2 ((phi_2)/2)`
` :. Phi_2 = (2pi)/3 = ((2pi)/lambda)(Deltax_2)= (2pi)/lambda ((y_2d)/D)`
`:. Y_2 = (lambdaD)/(3d) = beta/3 `
` Deltay = y_2 -y_1 = beta/12` .