Deriving the law of reflection from Fermat's principle

Step 1 of 4: Fermat's principle

Intuition

Light is as 'thrifty with time' as possible — like a firefighter choosing the fastest run to the hose and then to the fire.

t_{APB} = \frac{|AP| + |PB|}{c} \ \text{cực tiểu}

Analysis

In a homogeneous medium the light speed $c$ is constant, so minimizing time is the same as minimizing path length. The ray goes from $A$ , reflects at a point $P$ on the mirror, then reaches $B$ — the problem is to find $P$ minimizing the sum $|AP| + |PB|$ .