Answer
The difference in film thickness between points a and b is $~~\frac{\lambda}{2}$
Work Step by Step
The reflection of the light at point (a) results in a maximum.
The reflection of the light at point (b) is the next position that results in a maximum.
Therefore, the path length within the film at point (b) must be greater by one wavelength compared to the path length within the film at point (a).
Since light rays travel into the film and reflect off the back surface, the thickness of the film at point (b) must be greater by $\frac{\lambda}{2}$ compared to the thickness of the film at point (a).
The difference in film thickness between points a and b is $~~\frac{\lambda}{2}$
