In Young's double slit experiment intensity at a point is given by

$\mathit{\text{I}}={\mathit{\text{I}}}_0{\text{ cos}}^2\left(\frac{\varphi }{2}\right)$

where $\varphi$ = phase difference,

${\mathit{\text{I}}}_0$ = maximum intensity

or     $\frac{\mathit{\text{I}}}{{\mathit{\text{I}}}_0}={\text{cos}}^2\left(\frac{\varphi }{2}\right)$           .......(i)

Phase difference $\varphi =\frac{2\pi }{\lambda }\times \text{path difference}$

$\therefore$  $\varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{6}$   or $\varphi =\frac{\pi }{3}$   .......(ii)

Substitute equation (ii) in equation (i), we get

$\frac{\mathit{\text{I}}}{{\mathit{\text{I}}}_0}={\text{cos}}^2\left(\frac{\pi }{6}\right)$     or     $\frac{\mathit{\text{I}}}{{\mathit{\text{I}}}_0}=\frac{3}{4}$.