In Young's double slit experiment, intensity at a point is...

I = {I}_\max\cos^{2} \left(\dfrac{ϕ}{2}\right)

\dfrac{Imax}{4} = {I}_\max\cos^{2}\dfrac{ϕ}{2}

$cos$\dfrac{ϕ}{2} = \dfrac{1}{2}

\dfrac{ϕ}{2} = \dfrac{\pi}{3}

$⇒ ϕ =$\dfrac{2\pi}{3} = \left(\dfrac{2\pi}{λ}\right) \times \Deltax . . . . \left( i\right)$</p><p>where,$\Deltax = $dsin\theta</p><p>Putting the$value of\Deltax in$Eq. (i), we get</p><p>sin\theta =$\dfrac{λ}{3d}$</p><p>\theta = \sin^{- 1} \left(\dfrac{λ}{3d}\right)$