CBSE Class 12 Physics sample paper 2026-27: question 26

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Step-by-step solution

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1. Huygens' principle: every point on a wavefront is a source of secondary wavelets; the new wavefront is the common tangent (envelope) to these wavelets. Let a plane wavefront AB be incident at angle $i$ on the surface separating medium 1 (speed $v_1$) and medium 2 (speed $v_2$). (Figure: A touches the surface first; B is still in medium 1 at distance BC from the surface point C.)

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2. In time $t$, B reaches C: $BC=v_{1}t$. Meanwhile the wavelet from A spreads into medium 2 to radius $AE=v_{2}t$; the tangent CE is the refracted wavefront at angle $r$. From triangles ABC and AEC (common hypotenuse AC): $\sin i=\frac{BC}{AC}$, $\sin r=\frac{AE}{AC}$, so $\frac{\sin i}{\sin r}=\frac{v_{1}t}{v_{2}t}=\frac{v_1}{v_2}$. With $n=c/v$, $\frac{v_1}{v_2}=\frac{n_2}{n_1}$, giving $n_1\sin i=n_2\sin r$ — Snell's law.

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3. Prediction verified: wave theory predicts that light travels slower in a denser medium ($v_2<v_1$ when $n_2>n_1$). Foucault's experiment showed the speed of light in water is less than in air, confirming wave theory and contradicting the corpuscular theory.

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Answer: sin i/sin r = v₁/v₂ = n₂/n₁, i.e. n₁ sin i = n₂ sin r; speed of light is less in a denser medium (verified by Foucault).

Revise the chapter

• Chapter: Wave Optics (notes, formulas, where marks are lost and every past question)
• Topic: Huygens Principle and Wavefronts