In Young's double slit experiment intensity at a point is `((1)/(4))` of the maximum intersity. Angular position of this point is

Options

A. `sin^(-1)((lambda)/(d))`
B. `sin^(-1)((lambda)/(2d))`
C. `sin^(-1)((lambda)/(3d))`
D. `sin^(-1)((lambda)/(4d))`

Answer

C

Explanation

`I = I_(max) cos^(2) ((phi)/(2)) (I_(max))/(4) = I_(max) cos^(2) ((phi)/(2))`
`cos (phi)/(2) = (1)/(2) or ((phi)/(2)) = (pi)/(3)`
`phi = (2pi)/(3) = ((2pi)/(lambda)). Delta x` …(1) where `Delta x = d sin phi` Substituting in Eq. (1), we get
`sin phi = (lambda)/(3d) or q = sin^(-1) ((lambda)/(3d))`
correct answer is (C ).