Answer
Intensity is a maximum when $~~n = 1.8$
Work Step by Step
Note that the phase difference is $\frac{\lambda}{2}$ when $n = 1.4$ because the first minimum occurs when $n = 1.4$.
We can find an expression for $L$:
$phase~difference = 1.4~L-L = \frac{\lambda}{2}$
$L = \frac{\lambda}{0.8}$
$L = 1.25~\lambda$
We can find $n$ when the phase difference is $m~\lambda$, where $m$ is an integer:
$phase~difference = n~L-L = m \lambda$
$n-1 = \frac{m \lambda}{L}$
$n = 1+\frac{m \lambda}{1.25~\lambda}$
$n = 1+0.8~m$
$n = 1.8, 2.6,...$
Intensity is a maximum when $~~n = 1.8$
