L-21: Dispersion and Scattering of Light
Physics — Class 12 · NIOS Code 312 · Module 6 · Source: 312_Physics_Eng_Lesson21.pdf
Dispersion and Scattering of Light
When white light passes through a prism, colour bands appear — this is dispersion, distinct from ordinary refraction. Scattering explains why the sky is blue and the Sun looks red near the horizon. This lesson is part of Module 6 (Optics).
NIOS objectives: dispersion; prism deviation and μ; wavelength dependence; primary/secondary rainbows; scattering applications; Raman effect.
21.1 Dispersion of Light
Visible light is a small part of the EM spectrum. Sunlight contains seven wavelengths (VIBGYOR). In a dispersive medium, different wavelengths travel at different speeds → different μ → separation of colours. Air/vacuum are nearly non-dispersive for visible light.
μ depends on nature of material and wavelength λ. Spectral dispersive power: Δμ/Δλ.
21.1.1 Dispersion through a Prism
A glass slab does not show clear dispersion (emergent rays stay parallel to incident). A prism widely separates colours on a screen — forming a spectrum. Violet bends most; red least.
21.1.2 Angle of Deviation
A = refracting angle of prism
i, e = angles of incidence and emergence
r₁ + r₂ = A
Minimum deviation (δm): e = i; r₁ = r₂ = A/2; ray passes symmetrically parallel to base.
δm differs for each colour → dispersion
Emergent beam brightest at minimum deviation
Since μV > μR, we have δV > δR
μ increases as wavelength decreases
21.1.3 Angular Dispersion and Dispersive Power
Angular dispersion = δV − δR
δY ≈ mean deviation for yellow
Rainbow Formation
Sunlight dispersed by water droplets in air. With Sun behind observer, coloured arcs appear.
- Primary rainbow: 2 refractions + 1 internal reflection. Minimum deviation ~137°29′ → cone ~42° at eye. Outer edge red, inner violet (VIBGYOR).
- Secondary rainbow: 2 refractions + 2 internal reflections. Red inner, violet outer — colours reversed. Fainter; lies above primary. Dark band (Alexander's dark band) between them.
21.2 Scattering of Light in Atmosphere
21.2.1 Rayleigh Scattering
Interaction of radiation with particles much smaller than λ. Two-step process: absorption then re-emission in all directions (not reflection). Particle size must be < λ for wavelength-dependent scattering.
Shorter λ scattered much more intensely
Blue scattered ~6× more than red
Large droplets scatter all wavelengths equally → white
- Blue sky: air molecules scatter blue/violet more; eye less sensitive to violet → sky looks blue.
- White clouds: water droplets > λ scatter all colours equally.
- Dense clouds black: absorb sunlight rather than transmit.
- Red Sun at sunrise/sunset: long atmospheric path removes blue by scattering.
- Space: no scattering particles → sky black to astronauts.
- Deep blue after rain: dust removed; purer Rayleigh scattering.
21.2.2 Raman Effect
When light scatters from transparent solids, liquids, or gases, the scattered radiation may have frequency greater or less than incident frequency (discovered by C.V. Raman, 1928; Nobel Prize 1930).
- No energy exchange: frequency unchanged (Rayleigh scattering).
- Stokes lines: scattered frequency less than incident (light loses energy to substance).
- Anti-Stokes lines: scattered frequency greater than incident (substance in excited state gives energy to light).
Raman spectrum reveals molecular structure; analogue of Compton effect for X-rays.
DISPERSION & SCATTERING — KEY POINTS
=====================================
Dispersion : μ depends on λ; prism splits VIBGYOR
Min deviation : μ = sin((A+δm)/2)/sin(A/2)
Small prism : δ = (μ−1)A ; δV > δR
Dispersive power: ω = Δμ/μ
Primary rainbow : 2 refractions + 1 reflection (~42°)
Secondary bow : 2 refractions + 2 reflections (reversed)
Rayleigh scatter: I ∝ 1/λ⁴
Raman effect : Stokes & anti-Stokes frequency shifts
Quick Revision
- Dispersion = splitting by wavelength-dependent μ; prism not glass slab.
- Violet deviated most; red least; δV > δR.
- Minimum deviation gives μ from prism geometry.
- Primary rainbow: red outside; secondary: colours reversed, fainter.
- Rayleigh: I ∝ 1/λ⁴ explains blue sky and red Sun.
- Clouds white (large droplets); Raman effect shifts scattered frequency.
Q1. Dispersion of light occurs because:
Q2. In a prism spectrum, which colour is deviated the most?
Q3. For a small-angle prism, the angle of deviation is:
Q4. At minimum deviation in a prism:
Q5. A primary rainbow is formed by:
Q6. Compared to the primary rainbow, the secondary rainbow has:
Q7. According to Rayleigh's law, intensity of scattered light varies as:
Q8. The blue colour of the sky is mainly due to:
Q9. Clouds appear white because:
Q10. In the Raman effect, anti-Stokes lines have frequency:
PYQ — Previous Year Questions
Extracted from NIOS Physics (312) board exam papers in your PDF. Chapter L21 — Dispersion and Scattering of Light only. Use Model Answer for marking points; Explanation for concept clarity.
Chapter 21 — Dispersion and Scattering of Light (L21)
12 questions · Sections A & B · Sources: 312/TUS/104A, 312/MAY/204A, 312/MAY/204B, 68/ESS/1-312-A
Section A — Objective (1 mark)
PYQ1. In the sky after rains, rainbow is formed due to the phenomenon of (A) interference (B) diffraction (C) polarization (D) dispersion
Model Answer
(D) dispersion
Rainbow forms when sunlight undergoes refraction, internal reflection and again refraction in water droplets — different wavelengths deviate by different amounts (dispersion).
Explanation
Primary/secondary rainbows are dispersion phenomena in spherical drops (L21 §21.2). Interference/diffraction/polarization are wave phenomena but not the main cause of the coloured bow.
PYQ2. If we make identical prisms of different types of glass, the broadest spectrum is formed by a (A) soda glass prism (B) crown glass prism (C) flint glass prism (D) quartz glass prism
Model Answer
(C) flint glass prism
Flint glass has the highest dispersive power among common glasses → greatest angular separation of colours → broadest spectrum.
Explanation
Dispersive power ω = (μV − μR)/(μY − 1). Flint glass has larger μ variation with λ than crown/soda/quartz (L21 §21.1).
PYQ3. Which of the following colour of white light deviates the most when passes through a prism? (A) Red (B) Violet (C) Yellow (D) Green
Model Answer
(B) Violet
Shortest wavelength → highest refractive index in glass → largest angle of deviation.
Explanation
μ increases toward violet end of spectrum; δV > δR. Order in spectrum: VIBGYOR from base of prism outward (L21 §21.1).
PYQ4. The refracting angle of a prism is 30′ and its refractive index is 1.6. Calculate the deviation caused by the prism. (A) 28′ (B) 8′ (C) 30′ (D) 18′
Model Answer
Thin-prism formula: δ = (μ − 1) A
δ = (1.6 − 1) × 30′ = 0.6 × 30′ = 18′ → (D)
Explanation
For small refracting angle, δ ≈ (μ−1)A (L21 §21.1). 30′ = 0.5°; same result in arcminutes.
PYQ5. Read the passage: “Dispersion of light indicates that white light is composed of seven wavelength ranges corresponding to the seven colours of the rainbow.” The phenomenon responsible for the formation of rainbow is: (A) interference (B) diffraction (C) dispersion (D) polarization
Model Answer
(C) dispersion
Explanation
Passage links white light splitting into spectral colours with rainbow formation — both are dispersion (L21 §21.2).
Section A — Short Answer (2 marks)
PYQ6. Write ‘True’ for correct statement and ‘False’ for incorrect statement: (a) Angular dispersion for any two colours is independent of the angle of prism. (b) Angular width of primary rainbow is more than the angular width of secondary rainbow.
Model Answer
(a) False — angular dispersion (δV − δR) depends on prism angle A; for thin prism δ = (μ−1)A so dispersion ∝ A.
(b) False — secondary rainbow subtends a larger angle (~50°) than primary (~42°) about the antisolar point.
Explanation
Board T/F on dispersion geometry and rainbow cones (L21 §21.1–21.2). Do not confuse colour-band width inside each bow with overall angular radius.
PYQ7. Match Column—I with Column—II: (a) Formation of rainbow — (i) Interference (ii) Diffraction (iii) Scattering (iv) Dispersion; (b) Blue colour of sky — same options.
Model Answer
(a) Formation of rainbow → (iv) Dispersion
(b) Blue colour of sky → (iii) Scattering (Rayleigh scattering of sunlight by air molecules)
Explanation
Rainbow = wavelength-dependent refraction in drops. Blue sky = preferential scattering of short λ (I ∝ 1/λ⁴) — L21 §21.2.
PYQ8. Fill in the blanks (attempt any two parts): (i) A ray of light undergoes ______ twice on passing through a prism. (ii) ______ is the most scattered colour. (iii) The deviation through a prism is minimum when angle of incidence equals angle of ______. (iv) According to Rayleigh's law, intensity of scattered light is inversely proportional to the ______ power of wavelength.
Model Answer
(i) refraction (at the two refracting faces)
(ii) violet (or blue — shortest visible λ scattered most)
(iii) emergence (e = i at minimum deviation)
(iv) fourth (I ∝ 1/λ⁴)
Explanation
Prism optics + Rayleigh law blanks from ESS paper (L21 §21.1, §21.2.1). At δm, ray is symmetric inside prism: i = e, r₁ = r₂.
PYQ9. Name any two phenomena based on scattering of light.
Model Answer
Any two, e.g.:
- Blue colour of the sky
- Red colour of the Sun at sunrise/sunset
- Tyndall effect / reddening at horizon / deep blue sky after rain
Explanation
All arise from Rayleigh (or Tyndall) scattering — preferential deflection of shorter wavelengths by particles smaller than λ (L21 §21.2).
Section B — Short Answer (3 marks)
PYQ10. Draw a ray diagram showing the dispersion through an equiangular triangular glass prism. Write expression for the refractive index of the prism in terms of angle of minimum deviation and angle of prism. Why does the prism disperse rays of different colours at different angles?
Model Answer
Ray diagram: White ray incident on prism → emergent fan of coloured rays (VIBGYOR) with violet deviated most.
Refractive index: μ = sin((A + δm)/2) / sin(A/2)
Why dispersion: μ depends on wavelength (μV > μR) → different refraction angles → different deviations for each colour.
Explanation
Equiangular prism: symmetric geometry at minimum deviation gives the standard μ formula (L21 §21.1). Material dispersion causes colour separation.
PYQ11. Write expression for the refractive index of the material of a prism. Reduce the expression for a thin prism of small refracting angle. Calculate the angle of minimum deviation for a thin prism of refractive index 1.6 and refracting angle 1°.
Model Answer
General: μ = sin((A + δm)/2) / sin(A/2)
Thin prism (A small): δm = (μ − 1) A
Numerical: δm = (1.6 − 1) × 1° = 0.6°
Explanation
Small-angle reduction uses sin θ ≈ θ (radians) or direct proportionality δ ∝ (μ−1)A in degrees for thin prisms (L21 §21.1).
PYQ12. A glass prism of refracting angle 60° and refractive index 1.5 is completely immersed in water. Calculate the angle of minimum deviation of the prism in this situation. Given: refractive index of water = 1.33, sin⁻¹(0.56) = 34.38°.
Model Answer
Relative refractive index in water: μ′ = nglass/nwater = 1.5/1.33
μ′ = sin((A + δm)/2) / sin(A/2)
sin((60° + δm)/2) = (1.5/1.33) × sin 30° = 0.564
(60° + δm)/2 = sin⁻¹(0.56) = 34.38°
δm = 8.76° ≈ 8.8°
Explanation
Immersion changes effective μ to nprism/nsurround. Board gives sin⁻¹(0.56) = 34.38° to complete the calculation (L21 §21.1).
Problem Solving — L21 Dispersion and Scattering of Light
Six problems spanning this chapter’s NIOS syllabus. Every question is built from the notes and formula sheet: solve with equations first, then read the formal textbook-style write-up, the easy explanation, and the topic in depth (formulas, meaning, exam tips). Explanations open by default.
Why does a prism disperse white light into a spectrum?
Solution — step by step with formulas
- μ is larger for violet than red ⇒ greater deviation for violet.
Final answer: Different λ have different μ ⇒ different deviation
Formulas used in this problem
Textbook formal language
Dispersion arises because refractive index varies with wavelength.
Working formula set for this problem: μ depends on λ. In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Violet bends more than red in glass, so colours split.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Dispersion
Cauchy’s formula approximates μ(λ) for transparent media.
Link to chapter notes (L21 — Dispersion): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: μ depends on λ. In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write μ depends on λ before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Outline formation of a primary rainbow (dispersion + reflection).
Solution — step by step with formulas
- Sunlight enters raindrop, disperses, reflects internally once, exits—colours at different angles.
Final answer: Dispersion + one TIR-like internal reflection in drops
Textbook formal language
Geometric optics of spherical drops yields angular separation of colours.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Drops act like tiny prisms plus a mirror; red and violet leave at different angles.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Rainbow formation
Secondary rainbow involves two internal reflections.
Link to chapter notes (L21 — Rainbow formation): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Why is the clear sky blue according to Rayleigh scattering?
Solution — step by step with formulas
- Shorter λ (blue) scattered more strongly (∝1/λ⁴) by air molecules.
Final answer: Blue scattered more than red
Formulas used in this problem
Textbook formal language
Rayleigh scattering intensity varies as inverse fourth power of wavelength for particles ≪ λ.
Working formula set for this problem: I ∝ 1/λ⁴. In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Air molecules bounce blue light all over the sky; redder light goes more straight.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Rayleigh scattering
Valid for molecular sizes much smaller than optical wavelengths.
Link to chapter notes (L21 — Rayleigh scattering): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: I ∝ 1/λ⁴. In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write I ∝ 1/λ⁴ before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Explain red appearance of the Sun at sunrise/sunset.
Solution — step by step with formulas
- Long path through atmosphere; blue scattered out of line of sight; red/orange remains.
Final answer: Blue removed by long-path scattering
Textbook formal language
Optical path length in atmosphere is maximum near horizon.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Sunlight travels through more air; blue is scattered away, leaving warm colours.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Red sunset
Pollution can enhance red/orange hues.
Link to chapter notes (L21 — Red sunset): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
State the formula for refractive index of prism material in terms of A and δ_m.
Solution — step by step with formulas
- μ = sin((A+δ_m)/2) / sin(A/2).
Final answer: μ = sin((A+δ_m)/2)/sin(A/2)
Formulas used in this problem
Textbook formal language
Minimum deviation configuration is symmetric; yields standard μ formula.
Working formula set for this problem: δ = i + e − A; μ = sin((A+δ_m)/2)/sin(A/2). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Measure prism angle and least deviation, plug into the sine formula for μ.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Prism deviation
Used in spectrometer experiments.
Link to chapter notes (L21 — Prism deviation): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: δ = i + e − A; μ = sin((A+δ_m)/2)/sin(A/2). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write δ = i + e − A; μ = sin((A+δ_m)/2)/sin(A/2) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
What are complementary colours in the context of mixing light?
Solution — step by step with formulas
- Two colours that mix to produce white (e.g. blue + yellow light).
Final answer: Pair that yields white on addition
Textbook formal language
Additive mixing of spectral components can reconstitute white.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
If two coloured lights together look white, they complement each other.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Complementary colours
Distinct from subtractive mixing of pigments.
Link to chapter notes (L21 — Complementary colours): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).