Physics · Wave Optics · NEET
Because the incident and reflected waves are in the SAME medium, they travel at the same speed v. So in the same time tau, the distance BC (that B travels to reach the surface) equals the radius AE (that the wavelet from A spreads). This makes triangles ABC and EAC congruent: both are right-angled, they share the hypotenuse AC, and BC = AE = v times tau. Congruent triangles have equal angles, so i = r.
v is the speed of the wave in the medium and tau is the time taken by the wavefront to travel from B down to the surface at point C. So v times tau = BC = the distance B moves to reach the mirror. During that SAME time tau, the wavelet started earlier at A has spread a sphere of radius AE = v times tau. Both distances are equal because speed and time are the same.
Triangles ABC and EAC. Both have a right angle (angle ABC = 90 degrees at B on wavefront AB; angle AEC = 90 degrees where CE touches the wavelet). They share the common hypotenuse AC. And AE = BC = v times tau. By the RHS (right angle, hypotenuse, side) rule they are congruent, therefore angle BAC = angle ECA, which means i = r.
Neither changes. Reflection keeps the wave in the same medium, so speed v is unchanged, and frequency is set by the source, so it stays the same too. Since v = f times lambda and both v and f are constant, the wavelength lambda is also unchanged. Only the direction of travel of the wavefront changes.
Every point on the flat incident wavefront reaches the plane mirror one after another and each emits spherical secondary wavelets of the same radius pattern. Because the mirror is flat and the speed is uniform, the common tangent (envelope) of all these wavelets is again a flat plane CE. A plane incident wavefront on a plane surface gives a plane reflected wavefront.
The Huygens construction is drawn entirely in the plane of the page, which contains the incident ray direction, the normal to the mirror, and the reflected ray direction. Since the wavelets spread symmetrically and the tangent CE lies in this same plane, the incident ray, reflected ray and normal are all coplanar. This is the second law of reflection, obtained for free from the same figure.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
AE = BC = v times tau. The wavelet radius from A equals the distance B travels to the surface, because both happen in the same medium (same speed v) over the same time tau.
Both waves are in the same medium. Wave speed depends only on the medium, so it does not change on reflection. That is why the two triangles come out congruent and i = r.
Yes. The congruent triangles give i = r (first law), and the whole construction lying in one plane shows the incident ray, reflected ray and normal are coplanar (second law).
Plane. A plane incident wavefront striking a plane mirror produces a plane reflected wavefront, because the envelope of the equal spherical wavelets is a flat tangent plane.
No. Frequency is fixed by the source and does not change on reflection or refraction. In reflection wavelength also stays the same because speed is unchanged.
