"Dispersion and Scattering of Light"

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Why does white light split into a rainbow of colours through a prism? Why is the sky blue and the setting sun red? This chapter answers these questions through the phenomena of dispersion — the separation of light into its constituent colours — and scattering — the redirection of light by particles in its path.

Key Concepts

21.1 Dispersion of Light

Dispersion is the splitting of white light into its constituent colours when passing through a refracting medium. It occurs because the refractive index of a medium varies with wavelength.

Order of deviation (VIBGYOR): Violet deviated most → Red deviated least.

$n_{\text{violet}}>n_{\text{red}}$, so violet bends more.

Ordinary gases do NOT show dispersion with visible light because their refractive index is almost the same for all visible wavelengths — the variation is too small.

21.2 Factors Affecting Dispersion

• Angle of prism: Larger angle → more noticeable dispersion, greater spread
• Size of prism: Larger prism → longer path → wider spectrum
• Material: Key factor — dispersive power depends on the material

21.3 Prism Formula

At minimum deviation: $n=\frac{\sin \left(\frac{A+{\delta }_m}{2}\right)}{\sin (A/2)}$

Where $A$ = angle of prism, ${\delta }_m$ = angle of minimum deviation.

For an equilateral prism where ${\delta }_m=A=60°$: $n=\frac{\sin 60°}{\sin 30°}=\frac{\sqrt{3}/2}{1/2}=\sqrt{3}\approx 1.732$

21.4 Rainbow Formation

Primary rainbow: One internal reflection inside water droplet. Red on outer edge, violet on inner edge.

Secondary rainbow: Two internal reflections. Order reversed, fainter.

Rainbows are formed by dispersion, refraction, and total internal reflection of sunlight in water droplets.

21.5 Scattering of Light

Rayleigh scattering: Scattering by particles much smaller than wavelength. Intensity $\propto 1/{\lambda }^4$.

• Blue light ($\lambda \approx 450$ nm) scattered ~10× more than red ($\lambda \approx 700$ nm)
• Explains: blue sky, red sunsets

Mie scattering: Scattering by larger particles (dust, water droplets). Wavelength-independent.

• Explains: white clouds, grey/black dense clouds

Why is the sky blue? Air molecules scatter blue light more strongly.

Why is the sky deep blue after rain? Rain washes away dust — cleaner air means purer Rayleigh scattering, giving a deeper blue.

Why do dense clouds appear black? Thick clouds absorb and scatter nearly all light — very little reaches our eyes.

Why is the setting sun red? Sunlight travels through more atmosphere at sunset — blue light is scattered away, leaving red.

INTEXT QUESTIONS 21.1

Q1. Most ordinary gases do not show dispersion with visible light. Why?

Ans: Ordinary gases have almost the same refractive index for all visible wavelengths. The difference in speed between different colours is extremely small, so colours don't separate. Their molecular structure doesn't cause significant variation in refractive index.

Q2. Which colour is deviated more from its original direction through a prism?

Ans: Violet is deviated most (highest refractive index, shortest wavelength). Red is deviated least (lowest refractive index, longest wavelength). Order: Violet > Indigo > Blue > Green > Yellow > Orange > Red.

Q3. Does dispersion depend on the size and angle of the prism?

Ans: Yes. A larger refracting angle gives more noticeable dispersion (greater spread). A larger prism provides a longer path, making the spectrum wider and more distinct. But the material and refracting angle are the primary factors.

Q4. Calculate the refractive index of an equilateral prism if the angle of minimum deviation equals the angle of the prism.

Ans: $A=60°$, ${\delta }_m=60°$

$n=\frac{\sin \left(\frac{60°+60°}{2}\right)}{\sin (60°/2)}=\frac{\sin 60°}{\sin 30°}=\frac{\sqrt{3}/2}{1/2}=\sqrt{3}\approx 1.732$

INTEXT QUESTIONS 21.2

Q1. Why do dense clouds appear black?

Ans: Thick clouds contain large water droplets that absorb or multiply scatter most sunlight. Very little light reaches our eyes from their interiors — hence the dark/black appearance. Thin clouds scatter all wavelengths equally and appear white.

Q2. Why does the sky appear deep blue after rains on a clear day?

Ans: Rain washes away dust and particulate matter, leaving cleaner air with only small molecules (N₂, O₂). In clean air, Rayleigh scattering is purer and stronger — shorter wavelengths (blue) are scattered most efficiently, giving a deeper blue sky.

Terminal Exercise

1. What is dispersion of light? Explain with a prism. Why does violet deviate more than red?

2. Derive the prism formula: $n=\frac{\sin [(A+{\delta }_m)/2]}{\sin (A/2)}$.

3. Explain the formation of a rainbow. Why is it always circular?

4. Distinguish between Rayleigh scattering and Mie scattering. Give one example of each.

5. Explain why: (a) the sky is blue, (b) the setting sun appears red, (c) clouds appear white.

6. A prism of angle 60° produces a minimum deviation of 40°. Find its refractive index.

7. What is angular dispersion? How does it differ from dispersive power?

8. Why are danger signals red in colour?

9. Explain why the sky appears dark to astronauts in space.

10. What would be the colour of the sky if Earth had no atmosphere?

Quick Revision