Prisms and the Dispersion of Light

Introduction

Few natural sights are as captivating as a rainbow arching across the sky after a storm. Similarly, few classroom demonstrations spark as much wonder as a beam of white light spreading into a vibrant spectrum when it passes through a glass prism. Both phenomena share a common origin: dispersion of light.

A prism is a transparent optical element with flat, polished surfaces that refract light. When white light enters a prism, each color (or wavelength) bends differently, separating into a spectrum of red, orange, yellow, green, blue, indigo, and violet. This process, known as dispersion, reveals light’s hidden complexity and has profound implications for science, technology, and our understanding of nature.

This article explores the physics of prisms and dispersion in depth—covering historical discoveries, mathematical explanations, experimental demonstrations, and modern applications.

1. The Nature of Light

1.1 White Light and Its Components

White light, like sunlight, appears colorless but is actually a mixture of many wavelengths. The visible spectrum spans approximately 400 nanometers (violet) to 700 nanometers (red). Each wavelength corresponds to a different color that our eyes perceive.

1.2 Light as a Wave

Light behaves as an electromagnetic wave characterized by:

Wavelength (λ) – distance between successive crests.
Frequency (f) – cycles per second.
Speed (v) – product of wavelength and frequency (v = fλ).

When light enters a new medium, its frequency remains constant, but its speed and wavelength change, leading to refraction.

2. Refraction: The Foundation of Dispersion

Before understanding dispersion, we must revisit refraction—the bending of light when it moves between media of different optical densities.

The relationship between the incident and refracted angles is given by Snell’s Law: n1sin⁡θ1=n2sin⁡θ2n_1 \sin \theta_1 = n_2 \sin \theta_2n1sinθ1=n2sinθ2

where n1n_1n1 and n2n_2n2 are the refractive indices of the two media.

Crucially, refractive index depends on wavelength. This dependence, called chromatic dispersion, is what causes the spectrum to spread out in a prism.

3. Anatomy of a Prism

A prism is typically a solid block of transparent material—commonly glass or acrylic—shaped with flat polished sides. The most familiar is the triangular prism, usually with:

Two triangular end faces
Three rectangular side faces that meet at an angle (the apex angle).

When a light ray enters one face and exits through another non-parallel face, refraction occurs at both surfaces.

Key terms:

Angle of Incidence (i): Angle between incoming ray and normal to the first surface.
Angle of Refraction (r₁): Bending inside the prism.
Angle of Emergence (e): Angle at which the light exits.
Deviation Angle (D): Total angle between incident ray and emergent ray.

4. Dispersion of Light

Dispersion is the separation of white light into its component colors due to wavelength-dependent refraction.

4.1 Wavelength Dependence

The refractive index of most transparent materials decreases with increasing wavelength (normal dispersion).

Violet light (short λ) travels slowest in glass → bends most.
Red light (long λ) travels fastest → bends least.

This difference means the emergent beam fans out into a spectrum.

4.2 The Visible Spectrum

The classic sequence is remembered by the acronym ROYGBIV: Red, Orange, Yellow, Green, Blue, Indigo, Violet. However, the spectrum is continuous, with no strict boundaries.

5. Historical Background

Isaac Newton (1666): Conducted famous prism experiments in a darkened room, proving that white light is composed of many colors. He showed that prisms separate but do not create colors.
Earlier Observations: Ancient Greek and Arabic scholars noted color effects through glass, but Newton provided the first rigorous explanation.
Impact: Newton’s work laid the foundation for modern optics and color theory.

6. Mathematical Treatment

6.1 Deviation in a Prism

Consider a prism with apex angle AAA. For minimum deviation DmD_mDm: n=sin⁡(A+Dm2)sin⁡(A2)n = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}n=sin(2A)sin(2A+Dm)

where nnn is the refractive index for a given wavelength.

Because nnn depends on λ, each color emerges with a different deviation.

6.2 Angular Dispersion

The angular dispersion between two wavelengths λ₁ and λ₂ is: ΔD=D(λ1)−D(λ2)\Delta D = D(\lambda_1) – D(\lambda_2)ΔD=D(λ1)−D(λ2)

It quantifies how far apart the colors spread.

7. Types of Dispersion

Material Dispersion
Different wavelengths travel at different speeds in the same medium.
Geometric Dispersion
Depends on the prism’s apex angle and geometry.
Atmospheric Dispersion
Earth’s atmosphere acts like a giant prism, spreading starlight and causing stars to twinkle.

8. Experimental Demonstration

A classic classroom setup:

A dark room with a narrow slit and a white light source (sunlight or a strong lamp).
A triangular glass prism placed so light enters at an angle.
A white screen to capture the emergent spectrum.

As the prism is rotated to achieve minimum deviation, a brilliant spectrum appears on the screen.

9. Secondary Effects

9.1 Recombination of Colors

Newton used a second prism to recombine the spectrum into white light, proving that prisms separate but do not color the light.

9.2 Order of Colors

Shorter wavelengths always deviate more, hence violet appears at the bottom of a natural rainbow.

9.3 Dispersion in Lenses

Chromatic dispersion in lenses causes chromatic aberration, blurring images. Compound lenses of different glass types counteract this.

10. Applications of Prisms and Dispersion

10.1 Spectroscopy

Prisms are central to spectroscopes, which analyze the composition of light from stars, flames, or chemicals.

Astronomers identify elements in distant galaxies through spectral lines.
Chemists determine material composition by examining emitted light.

10.2 Optical Instruments

Binoculars and Cameras: Roof prisms and Porro prisms redirect light paths for compact design.
Periscopes: Submarines use prisms instead of mirrors to avoid image inversion.

10.3 Communication and Technology

Fiber optics exploit controlled dispersion for high-speed data transmission. Though modern systems often use diffraction gratings, prism-based spectrometers remain vital in laboratories.

10.4 Art and Aesthetics

Artists and designers use prisms to create dazzling lighting effects in architecture and stage shows.

11. Atmospheric Phenomena

11.1 Rainbows

Raindrops act as tiny spherical prisms, refracting and internally reflecting sunlight to form rainbows.

Primary Rainbow: One internal reflection; red outside, violet inside.
Secondary Rainbow: Two reflections; colors reversed.

11.2 Halos and Sundogs

Ice crystals in the upper atmosphere create halo rings around the sun or moon by prism-like refraction.

12. Advanced Concepts

12.1 Abnormal Dispersion

Some materials show regions where refractive index increases with wavelength (opposite to normal). Used in special optical filters and lasers.

12.2 Prism Materials

Crown glass: Common, low dispersion.
Flint glass: Higher dispersion, used when a wider spectrum is desired.
Quartz: Transparent to ultraviolet, used in UV spectroscopy.

12.3 Combination Prisms

Amici Prism: Produces a direct-view spectrum.
Pellin–Broca Prism: Rotated to select a specific wavelength while keeping the exit beam fixed.

13. Calculations: Example

Suppose a triangular prism of apex angle 60° produces a minimum deviation of 40° for yellow light.
Refractive index: n=sin⁡(A+D2)sin⁡(A2)n = \frac{\sin\left(\frac{A + D}{2}\right)}{\sin\left(\frac{A}{2}\right)}n=sin(2A)sin(2A+D) n=sin⁡(60+402)sin⁡30∘=sin⁡50∘0.5≈0.7660.5≈1.53n = \frac{\sin\left(\frac{60 + 40}{2}\right)}{\sin 30^\circ} = \frac{\sin 50^\circ}{0.5} \approx \frac{0.766}{0.5} \approx 1.53n=sin30∘sin(260+40)=0.5sin50∘≈0.50.766≈1.53

Typical of crown glass.

For violet light the deviation might be 42°, giving n ≈ 1.56, illustrating wavelength dependence.

14. Design Considerations

Engineers select prism materials and apex angles to achieve desired dispersion while minimizing absorption. Coatings reduce surface reflection losses. Temperature control is important because refractive index varies slightly with temperature.

15. Beyond the Visible Spectrum

Prisms can disperse infrared and ultraviolet light if the material is transparent at those wavelengths. This capability is essential for:

Infrared spectroscopy in chemical analysis.
Ultraviolet astronomy to study hot stars.

16. Cultural and Symbolic Roles

Prisms have captured the human imagination:

The iconic Pink Floyd “Dark Side of the Moon” album cover.
Architectural installations where prisms project shifting rainbows across interior spaces.
Metaphors in literature for clarity and revelation.

17. Challenges and Modern Alternatives

While prisms are invaluable, diffraction gratings often replace them in high-resolution spectroscopy because gratings can provide greater dispersion over a broader range. However, prisms remain essential for their durability, simplicity, and ability to work without overlapping spectral orders.

18. Summary of Key Points

A prism refracts light twice—on entry and exit—causing dispersion because refractive index varies with wavelength.
Violet light bends most; red least, producing a spectrum.
Newton proved that white light is composed of many colors.
Applications span spectroscopy, optics, communication, art, and atmospheric phenomena like rainbows.