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Wave Optics
Physics · Class 12 · Part 2NCERT pp. 255–2712 sets × 25 questionsFree
Key facts and formulas for Wave Optics, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Speed and wavelength in a medium | v = c / n, λ = λ₀ / n, frequency does not change |
| Phase and path difference | φ = 2π Δ / λ; bright if Δ = nλ, dark if Δ = (n + ½)λ |
| Two-beam intensity | I = 4 I₀ cos²(φ/2) for equal coherent waves; incoherent sources add: I = I₁ + I₂ |
| Fringe width | β = λ D / d; nth bright at nβ, nth dark at (n + ½)β |
| Max / min intensity | I_max / I_min = (a₁ + a₂)² / (a₁ − a₂)²; visibility = 2√(I₁I₂)/(I₁ + I₂) |
| Single slit | Minima: a sin θ = nλ (n ≠ 0); first minimum y = λ D / a; central width = 2λD/a |
| Resolution | θ_min = 1.22 λ / a for a circular aperture |
| Malus’s law and polaroids | I = I₀ cos²θ; unpolarised light through a polaroid gives I / 2 |
| Brewster’s law | tan i_p = μ; i_p + r = 90°; reflected light is plane polarised |
| Thin films and sheets | Sheet shift = (μ − 1) t / λ fringes; film bright: 2μt = λ/2 (one π change); Newton’s ring D ∝ √n |
Three sample questions
Q1. A ray bends towards the normal when entering a second medium. Which statement is correct?
- Both models predict lower speed there
- The wave model predicts lower speed there, while the corpuscular model predicts higher speed
- Both models predict higher speed there
- The wave model predicts higher speed there, while the corpuscular model predicts lower speed
Hint and solution
Hint: A ray bending towards the normal means the new medium is denser. Recall what each model says about speed in a denser medium.
- Bends towards normal → denser medium — A ray bends towards the normal when it enters a denser medium, where refractive index is larger.
- Wave model: v = c / n, so v decreases — In the wave model the speed in a medium is c divided by n, so light is slower in the denser medium.
- Corpuscular model: v increases — Newton’s particle picture explained bending by an attraction pulling corpuscles faster in the denser medium.
- Foucault: light slower in water — The two models predict opposite speeds, and the measurement favoured the wave model. So the answer is the second statement. Option B.
Answer: B. The two models give opposite predictions. Foucault found light slower in water, supporting the wave model.
Q2. Statement I: A wavefront is a surface of constant phase. Statement II: Energy flows along the wavefront, not across it.
- Statement I is true and Statement II is false
- Both statements are true
- Statement I is false and Statement II is true
- Both statements are false
Hint and solution
Hint: Ask which direction a ray points relative to the wavefront, and which way energy travels.
- Wavefront = surface of constant phase — Every point on a wavefront oscillates in the same phase, so Statement I is true.
- Ray ⟂ wavefront — A ray is drawn perpendicular to the wavefront and shows the direction of propagation.
- Energy flows along the ray — So energy moves across the wavefront, not along it. Statement II is false.
- I true, II false — Statement I is true and Statement II is false. Option A.
Answer: A. Energy flows perpendicular to the wavefront, along the ray. So II is false.
Q3. In Huygens construction in a medium of refractive index n, the radius of a secondary wavelet after time t is
- c t n
- n t / c
- c t / n
- c / (n t)
Hint and solution
Hint: The radius of a wavelet is speed multiplied by time. What is the speed of light in a medium of index n?
- n = c / v — Refractive index is the ratio of speed in vacuum to speed in the medium.
- v = c / n — So the speed of light in the medium is c divided by n.
- radius = v t = c t / n — A wavelet spreads out with speed v for a time t, so its radius is v times t.
- radius = c t / n — So the radius is c t divided by n. Option C.
Answer: C. Speed in the medium is c / n, so radius = v t = c t / n.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.