When I was solving questions on Ray optics I encountered a question wherein I had to prove that when a ray of light undergoes minimum deviation through a triangular prism then both the angles of refraction that is the first one at the incident point and the second one at the emergent point should be equal.
Since I was not able to prove this, I looked into the solution for this problem and it was written that for minimum deviation to take place in a triangular prism the angles of incidence that is the angle which the incident ray makes with the normal at that point and the angle of emergence that is the angle which the emergence ray makes with the normal at the point of emergence should be equal.
I could not access why this would happen.
Best Answer
The intuitive answer uses symmetry.
For a prism (or any linear optics) you should be able to reverse the direction of light and get the same result. This means that if a given angle of incidence $\alpha$ results in a certain exit angle $\beta$, then incident angle $\beta$ will result in exit angle $\alpha$.
Now a maximum or minimum in the deviation occurs when a small change doesn't change the outcome. By symmetry this has to happen when $\alpha=\beta$.