# Applying Fermat's principle in Fraunhofer's diffraction

The following set up with a source, 2 convex lenses, a slit and a screen is of that of Fraunhofer's diffraction:

*Correction S is not on the common optical axis, but above it.

$$\theta$$ = Angle between ray passing through midpoint(B) and the common optical axis(which also passes through B)

$$a$$ = Length of AC (A and C being the extremes of the slit)

When finding the point of 1st minima, we equate the optical path difference between 2 rays passing parallel through the slit at a distance of $$\frac{a}{2}$$ to $$(2n-1)\frac{\lambda}{2}$$, i.e $$\frac{a}{2} \sin\theta = \frac{\lambda}{2}$$

But according to Fermat's Principle of Least time, don't all the paths take the same amount of time(the least time = $$\tau$$) to travel from S to P and hence the optical path should be the same for all the paths = $$c\tau$$ , so why is there a difference in optical path?

• Fermat's principle gives the ray approximation to the optical field and this approximation ignores all wave effects such as difraction and interference. Commented Apr 5 at 18:24