A ray of light from a monochromatic point source of light is...

Let the original geometric path length be $x$.

Before the introduction of the mica film, the optical path is $x$ (assuming the medium is air or vacuum with refractive index $1$).

When a mica film of thickness $t$ and refractive index $n$ is introduced, the light travels a distance $x - t$ in air and a distance $t$ in the mica film.

The new optical path is $(x - t) \times 1 + t \times n = x + (n - 1)t$.

The change in the optical path is $(x + (n - 1)t) - x = (n - 1)t$.

Thus, the optical path is increased by $(n - 1)t$.

Answer: is increased by (n-1) t.