Physics · Wave Optics · NEET
Take a plane wavefront AB hitting surface PP' at angle i. In time tau, edge B travels distance BC = v1 x tau in medium 1 and reaches C. During the same time tau, edge A enters medium 2 and travels AE = v2 x tau. Draw the refracted wavefront CE. Now in right triangle ABC, sin i = BC/AC = v1 tau / AC. In right triangle AEC, sin r = AE/AC = v2 tau / AC. Divide them: sin i / sin r = v1/v2. Since v1 = c/n1 and v2 = c/n2, this becomes sin i / sin r = n2/n1, i.e. n1 sin i = n2 sin r. That is Snell's law.
The two edges of the wavefront do not reach the boundary at the same time. One edge crosses into the new medium first and changes speed, while the other edge is still moving in the old medium at the old speed. Because the two ends now travel different distances in the same time tau, the line joining them (the new wavefront) tilts. Bending happens only because the speed changes, not because the frequency changes.
sin i comes from the distance the wave travels in medium 1 (BC = v1 tau) and sin r comes from the distance in medium 2 (AE = v2 tau). Both are divided by the same hypotenuse AC. So sin i / sin r = (v1 tau / AC) / (v2 tau / AC) = v1/v2. Careful: in terms of refractive index this flips, sin i / sin r = n2/n1, because n is inversely proportional to speed (n = c/v).
It slows down. In a denser medium (higher n) the speed v = c/n is smaller. So v2 < v1, which makes sin r < sin i, meaning r < i. The refracted ray bends towards the normal. Huygens' wave theory predicts speed decreases in the denser medium, which matched experiment. Newton's corpuscular model wrongly predicted speed increases, so Huygens was right.
AB is the incident plane wavefront. tau is the small time taken for edge B to reach the boundary at C. BC = v1 x tau is how far the wave moves in medium 1. AE = v2 x tau is how far it moves in medium 2 (a sphere of radius v2 tau drawn from A). CE is the tangent plane = the refracted wavefront. AC is the common hypotenuse shared by both right triangles, which is why it cancels when you take the ratio.
Frequency is set by the source and cannot change when light crosses a boundary. Since v = f x lambda and f is fixed, when v decreases in a denser medium, lambda must decrease too. NCERT shows BC = lambda1 and AE = lambda2, and lambda2/lambda1 = v2/v1 = n1/n2. So in glass (n = 1.5), the wavelength shrinks to two-thirds while the colour (frequency) stays the same.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
n1 sin i = n2 sin r, which is Snell's law. Equivalently sin i / sin r = v1/v2 = n2/n1 = lambda1/lambda2.
Yes. The derivation gives v2 = v1 x (sin r / sin i). For air to glass, r < i so sin r < sin i, hence v2 < v1. Light slows in the denser medium, confirming the wave theory over Newton's corpuscular prediction.
No. Frequency is fixed by the source. Only speed and wavelength change (both drop in a denser medium), keeping v = f lambda consistent.
It stays a plane wavefront (CE is a straight tangent plane), but it is tilted at the angle of refraction r to the boundary because the two media have different speeds.
AC is the hypotenuse common to both right triangles ABC and AEC. Since sin i and sin r are both measured against the same AC, it cancels when you divide, leaving only the ratio of the distances v1 tau and v2 tau.
