Answer
$2\mu L$
Work Step by Step
The path length difference is $2 \mu L$, where $\mu$ is the refractive index of the thin film.
\begin{equation}
Path difference = c \times t .
\end{equation}
Here $c$ is the speed of light and t is the time taken by ray $r_4$ to travel a distance $2L$.
$t=\frac{2L}{v}$ where v is the velocity of light in the film.
From equation (1) path difference
\begin{equation}
=c \times \frac{2L}{v}
\end{equation}
refractive index of film material , $\mu = \frac{c}{v} $
Therefore path difference of $r_4=2\mu L$.
