Q.Prove the laws of reflection using Huygens' principle.

Step 1. A plane wavefront $AB$, perpendicular to incident rays $L,M$, strikes a plane mirror $XY$ obliquely; point $A$ reaches the mirror before point $B$ (since the wavefront is tilted relative to the mirror).

Step 2. By the time $B$ reaches the mirror at $B'$, $A$'s own secondary wavelet, launched the instant $A$ touched the mirror, has expanded outward by exactly the same distance $BB'$ has been travelled by $B$ (both travel the same speed, for the same elapsed time, in the same medium): $AA'=BB'$. The new reflected wavefront is the tangent line $A'B'$ to this and every other secondary wavelet along the mirror.

Step 3. Consider the two right triangles $\triangle ABB'$ and $\triangle B'A'A$: both share the same hypotenuse $AB'$; both have a right angle (at $B$ for the first, at $A'$ for the second, since the wavefronts are perpendicular to their respective rays); and their other two legs are equal, $AA'=BB'$ (Step 2). By the RHS (right angle-hypotenuse-side) congruency rule, the two triangles are congruent. …

Construct the reflected wavefront from secondary wavelets and show the resulting two right triangles (sharing a hy …

• Not clearly identifying which angles in the two congruent triangles correspond to the angle of incidence and angle of reflection. …