In Young's double slit experiment, light from two identical sources...

Given the path difference is $∆ x = \dfrac{7\lambda}{4}$

Hence, the phase difference can be found as follows:

$\begin{cases}ϕ & = & \dfrac{2\pi}{\lambda} ∆ x \\ & = & \dfrac{2\pi}{\lambda} \times \dfrac{7\lambda}{4} \\ & = & \dfrac{7\pi}{2}\end{cases}$

The formula to calculate the intensity is given by

I = {I}_\max\cos^{2}\left(\dfrac{ϕ}{2}\right) . . . \left(1\right)

From equation (1), it follows that

\begin{cases}\dfrac{I}{{I}_\max} & = & \cos^{2}\left(\dfrac{ϕ}{2}\right) \\ & = & \cos^{2}\left(\dfrac{7\pi}{2 \times 2}\right) \\ & = & \cos^{2}\left(\dfrac{7\pi}{4}\right) \\ & = & \cos^{2}\left(2\pi - \dfrac{\pi}{4}\right) \\ & = & \cos^{2}\dfrac{\pi}{4} \\ & = & \dfrac{1}{2}\end{cases}