Why Does a Prism Disperse Light? The Science of Rainbow Creation
Discover how white light splits into beautiful colors through the magic of dispersion, angular separation, and pure spectrum formation.
The Magic Behind the Colors
When Isaac Newton first passed sunlight through a prism in 1666, he unlocked one of physics' most beautiful phenomena - dispersion. But what exactly causes white light to separate into the vibrant colors of VIBGYOR?
🎯 JEE Relevance
Dispersion appears in every JEE paper, often as 2-3 mark questions testing conceptual understanding of refractive index dependence on wavelength and angular dispersion calculations.
🔍 Quick Navigation
1. The Fundamental Concept: What is Dispersion?
Definition
Dispersion is the phenomenon of splitting of white light into its constituent colors when it passes through a transparent medium.
🌈 Simple Analogy
Think of white light as a team of 7 runners (VIBGYOR colors) with different speeds. When they enter a muddy field (the prism), faster runners (violet) get slowed down more than slower runners (red), causing them to spread out.
Newton's Classic Experiment
Setup
Apparatus: Glass prism, white light source, screen
Observation: White light enters → Color spectrum emerges
Color Order: Red, Orange, Yellow, Green, Blue, Indigo, Violet
Key Discovery
Newton proved that:
- Different colors have different refractive indices in the same medium
- Violet light bends the most, red light bends the least
- Colors are property of light, not property of prism
2. The Heart of Dispersion: Refractive Index & Wavelength
Cauchy's Formula
The refractive index (μ) of a material depends on the wavelength (λ) of light according to Cauchy's formula:
Cauchy's Formula
Where A, B, C are material constants and λ is wavelength
What This Means
Since B is positive for most materials, μ decreases as λ increases. Therefore:
Red Light (λ ≈ 700 nm)
Long wavelength → Smaller μ → Less bending
Violet Light (λ ≈ 400 nm)
Short wavelength → Larger μ → More bending
Why Different Refractive Indices?
The Physics Behind It
When light enters a medium:
- Light waves interact with electrons in the material
- Electrons oscillate and re-radiate light
- This interaction depends on frequency (color)
- Higher frequency (violet) → Stronger interaction → Slower speed → Higher μ
- Lower frequency (red) → Weaker interaction → Faster speed → Lower μ
Mathematical Relationship
From electromagnetic theory:
Where c = speed in vacuum, v = speed in medium
Since violet light travels slower in glass than red light:
$v_{violet} < v_{red}$ ⇒ $μ_{violet} > μ_{red}$
3. Angular Dispersion: The Color Separation
Definition
Angular dispersion is the angular separation between extreme colors (red and violet) of the spectrum.
Angular Dispersion Formula
Derivation & Understanding
For Small Angle Prism
Using prism formula for small angles:
Deviation for red light: $\delta_R = A(\mu_R - 1)$
Deviation for violet light: $\delta_V = A(\mu_V - 1)$
Angular dispersion: $\theta = \delta_V - \delta_R = A(\mu_V - \mu_R)$
Numerical Example
Given: Prism angle A = 60°, $\mu_V = 1.665$, $\mu_R = 1.645$
Calculate: Angular dispersion θ
$\theta = A(\mu_V - \mu_R) = 60° × (1.665 - 1.645) = 60° × 0.02 = 1.2°$
The red and violet rays are separated by 1.2 degrees.
💡 Key Insight
Angular dispersion depends on:
- Prism angle (A) - Larger angle → More dispersion
- Material property ($\mu_V - \mu_R$) - Larger difference → More dispersion
- It's independent of the size of prism - Only shape matters!
4. Pure Spectrum: Perfect Color Separation
What is a Pure Spectrum?
A pure spectrum is one in which colors are perfectly separated without overlapping. Each wavelength appears as a distinct, sharp image.
🔬 Comparison
✓ Pure Spectrum
- Colors don't overlap
- Sharp boundaries
- Each λ has unique position
- Requires special setup
✗ Impure Spectrum
- Colors overlap
- Fuzzy boundaries
- Mixed colors appear
- Simple prism gives this
Creating a Pure Spectrum
Apparatus Setup
- Slit: Narrow slit to get parallel beam
- Collimating Lens: Makes light rays parallel
- Prism: At minimum deviation position
- Telescope: To view the spectrum
Why This Setup Works
- Narrow slit → Each color comes from specific direction
- Parallel rays → Each color focuses at unique point
- Minimum deviation → Symmetric path reduces aberrations
- Telescope focusing → Sharp image formation
🎯 JEE Application
Questions often ask:
- "Why does a simple prism not give pure spectrum?"
- "What modifications are needed for pure spectrum?"
- "Calculate angular dispersion for given parameters"
- "Compare refractive indices for different colors"
🌈 Nature's Prism: How Rainbows Form
In Raindrops
- Water droplets act as tiny prisms
- Light refracts, reflects internally, refracts again
- Different colors emerge at different angles
- Red appears at 42°, violet at 40° from anti-solar point
Key Differences from Prism
- Rainbow has red on top, violet at bottom
- Prism gives violet on top, red at bottom
- Rainbow involves total internal reflection
- Secondary rainbow has reversed colors
📋 Quick Revision Guide
Key Formulas
- Cauchy's formula: $\mu = A + \frac{B}{\lambda^2}$
- Angular dispersion: $\theta = A(\mu_V - \mu_R)$
- Dispersive power: $\omega = \frac{\mu_V - \mu_R}{\mu_Y - 1}$
- Deviation: $\delta = A(\mu - 1)$ (small angles)
Must Remember
- Violet bends most (highest μ)
- Red bends least (lowest μ)
- Angular dispersion ∝ prism angle
- Pure spectrum needs parallel rays
🎯 Practice Problems
1. A prism of angle 60° has μ₍ᵥ₎ = 1.5 and μ₍ᵣ₎ = 1.48. Calculate angular dispersion.
2. Why does violet light deviate more than red light in a prism?
3. What modifications are needed to obtain pure spectrum from a prism?
Mastered Prism Dispersion?
You now understand the beautiful physics behind rainbows and color separation!