Newton’s Theory of Light (Corpuscular Theory): A Comprehensive

Analysis
Vaftsy CAE
10 January 2012

Contents
1 Introduction 2
1.1 Core Postulates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Extensive Biography of Sir Isaac Newton 2

2.1 Early Life and Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 The Plague Years (1665-1667): Annus Mirabilis . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.3 Academic Career and Optical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.4 Rivalry with Robert Hooke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Historical Development and Context 3

3.1 Mechanical Philosophy Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4 Mathematical Framework and Equations 3

4.1 Snell’s Law from Corpuscular Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.2 Velocity Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.3 Color and Particle Size Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

5 Detailed Theoretical Derivations 4

5.1 Refraction Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5.2 Reflection Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

6 Enhanced Diagrams with TikZ 4

6.1 Basic Refraction Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
6.2 Advanced Prism Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
6.3 Reflection Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

7 Real-World Applications and Legacy 5

7.1 Contemporary Relevance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7.2 Smartphone Camera Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

8 Major Criticisms and Limitations 5

8.1 Fundamental Flaws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
8.2 Mathematical Inconsistencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

9 The Challenge: Young’s Double-Slit Experiment (1801) 6

9.1 Experimental Setup and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9.2 Theoretical Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

10 Transition to Wave-Particle Duality 6

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11 Enhanced Problem Sets 7
11.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

12 Advanced Assignment Problems 7

13 Historical Impact and Modern Perspective 7

14 References 8

1 Introduction
Sir Isaac Newton’s corpuscular theory of light, formulated in the late 17th century, proposed that light
consists of small particles called **corpuscles** that travel in straight lines at high speeds. This theory dom-
inated optical science for over a century before being challenged by wave theories and eventually reconciled
through wave-particle duality[12][7].

1.1 Core Postulates

Newton’s theory was based on the following fundamental assumptions[1]:

1. Light sources emit minute, elastic, rigid, and massless particles called corpuscles
2. These particles travel through transparent media at very high speeds in straight lines
3. Different colors correspond to corpuscles of different sizes
4. Corpuscles are repelled by reflecting surfaces and attracted by transparent materials

5. Vision occurs when these particles enter our eyes

2 Extensive Biography of Sir Isaac Newton

Sir Isaac Newton (1642-1727) was born prematurely on Christmas Day in Woolsthorpe, Lincolnshire, Eng-
land, just three months after his father’s death. His mother, Hannah Ayscough, remarried when Isaac was
three, leaving him with his grandmother[2][5][8].

2.1 Early Life and Education

Newton’s early academic performance was described as ”idle” and ”inattentive,” leading to his temporary
removal from grammar school in Grantham. However, his uncle recognized his potential and prepared him
for Trinity College, Cambridge, where he enrolled in 1661, somewhat older than his classmates[2][8].

2.2 The Plague Years (1665-1667): Annus Mirabilis

During the plague outbreak that closed Cambridge University, Newton returned to Woolsthorpe. These two
years became his **annus mirabilis** (miracle years), during which he developed:
• The foundations of calculus

• Theories of optics and color

• Laws of motion and universal gravitation
• Initial work on his corpuscular theory of light[2][5]

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2.3 Academic Career and Optical Work
Returning to Cambridge in 1667, Newton was appointed Lucasian Professor at the remarkably young age of
27. From 1670-1672, he delivered lectures on optics, investigating light refraction and demonstrating that
prisms separate white light into spectra[5][8].

2.4 Rivalry with Robert Hooke

Newton’s relationship with Robert Hooke was contentious. When Hooke criticized Newton’s optical theories,
Newton became so offended that he withdrew from public debate. This rivalry delayed the publication of
”Opticks” until after Hooke’s death in 1703[2][5].

3 Historical Development and Context

Newton’s corpuscular theory was published in **”Opticks”** (1704), challenging Christiaan Huygens’ wave
theory of light. The theory built upon the mechanical philosophy of the 17th century Scientific Revolution,
which described the universe in terms of matter and motion based on atomistic principles[12][10].

3.1 Mechanical Philosophy Background

The corpuscular theory emerged from the broader **mechanical philosophy** (1610-1650) that replaced Aris-
totelianism. This philosophy, based on Epicurean atomism, described everything in the universe—including
thoughts and souls—as composed of moving matter particles[12].

4 Mathematical Framework and Equations

4.1 Snell’s Law from Corpuscular Perspective
Newton derived Snell’s law by assuming corpuscles change speed when entering different media:

n1 sin θ1 = n2 sin θ2 (1)

where the refractive index n relates to corpuscle speeds:

c
n= (2)
vmedium

4.2 Velocity Relations

According to Newton’s theory, corpuscles move faster in denser media:

vdenser > vrarer (3)

This prediction was later proven experimentally incorrect[1].

4.3 Color and Particle Size Relationship

Newton proposed that different colors correspond to different corpuscle sizes:

λ ∝ corpuscle size (4)

where λ represents the characteristic wavelength associated with each color[7].

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5 Detailed Theoretical Derivations
5.1 Refraction Mechanism
Newton assumed corpuscles experience forces at media interfaces. Upon entering a denser medium, the
perpendicular velocity component changes while the parallel component remains constant:

v∥,1 = v∥,2 (5)

v⊥,2 = v⊥,1 + ∆v⊥ (6)

This leads to the refraction angle relationship:

sin θ1 v1
= (7)
sin θ2 v2

5.2 Reflection Analysis

For reflection, Newton proposed that corpuscles are repelled by the surface with equal and opposite momen-
tum:
θincident = θref lected (8)

6 Enhanced Diagrams with TikZ

6.1 Basic Refraction Diagram

Normal
Air (n1 = 1.0)
Incident corpuscles

θ1
θ2

Glass (n2 = 1.5) Refracted corpuscles

Figure 1: Corpuscular refraction showing particle paths and speed changes

6.2 Advanced Prism Dispersion

Red (large)
White light corpuscles
Spectrum

Violet (small)

Figure 2: Prism dispersion showing different corpuscle sizes for different colors

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6.3 Reflection Mechanism

Normal
Incident Reflected

θi Repulsive
θr forces

Reflecting Surface

Figure 3: Corpuscular reflection showing repulsive forces at the surface

7 Real-World Applications and Legacy

Despite its eventual supersession, Newton’s corpuscular theory has influenced modern applications[1]:

7.1 Contemporary Relevance

• Particle Optics: Electron microscopy uses particle-like behavior
• Ray Tracing: Computer graphics and optical design

• Photonics: Laser technology and fiber optics

• Quantum Optics: Foundation for photon concepts

7.2 Smartphone Camera Technology

Modern smartphone cameras use ray-tracing algorithms derived from corpuscular concepts for:
• Lens design optimization
• Autofocus mechanisms

• Computational photography

8 Major Criticisms and Limitations

Newton’s corpuscular theory faced significant challenges that ultimately led to its replacement[1]:

8.1 Fundamental Flaws

1. Partial Reflection and Refraction: The theory couldn’t explain why some light reflects while some
refracts simultaneously at interfaces

2. Wave Phenomena: Complete failure to explain interference, diffraction, and polarization

3. Velocity Predictions: Predicted higher light speed in denser media (experimentally disproven)
4. Mass Conservation: Light sources should lose mass when emitting corpuscles (not observed)
5. Rectilinear Propagation: Couldn’t explain bending around obstacles

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8.2 Mathematical Inconsistencies
The theory predicted that light velocity in water should be greater than in air:
vwater > vair (Newton’s prediction - INCORRECT) (9)
However, experiments showed:
vwater < vair (Experimental reality) (10)

9 The Challenge: Young’s Double-Slit Experiment (1801)

Thomas Young’s groundbreaking experiment delivered a devastating blow to Newton’s corpuscular the-
ory[3][6][9][11][13].

9.1 Experimental Setup and Results

Young’s experiment demonstrated clear interference patterns that could only be explained by wave behavior:

Screen

Light Source
Slit 1 Interference
Pattern
Bright
Dark
Slit 2

Figure 4: Young’s Double-Slit Experiment showing wave interference

9.2 Theoretical Implications

The experiment showed that if light were particles:
Expected pattern = Two spots (11)
But the observed pattern was:
Actual pattern = Alternating bright and dark fringes (12)
The fringe width is given by:
λD
w= (13)
d
where λ is wavelength, D is screen distance, and d is slit separation[6].

10 Transition to Wave-Particle Duality

The eventual resolution came through quantum mechanics, recognizing that light exhibits both particle and
wave properties depending on the experimental context[9][11]:
hc
E = hν = (14)
λ
This led to the modern photon concept, validating aspects of Newton’s particle intuition while incorpo-
rating wave behavior.

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11 Enhanced Problem Sets
11.1 Solved Examples
Example 1: Light travels from air (n = 1.0) to water (n = 1.33). If the incident angle is 30°, find the
refraction angle using Newton’s corpuscular model.
Solution: Using Snell’s law: n1 sin θ1 = n2 sin θ2 1.0 × sin(30) = 1.33 × sin θ2 0.5 = 1.33 × sin θ2
sin θ2 = 0.376 θ2 = 22.1
Example 2: According to Newton’s theory, if red corpuscles are larger than blue ones, explain prism
dispersion.
Solution: Newton proposed that larger corpuscles (red) experience different forces than smaller ones
(blue) when entering the prism, causing different deflection angles and creating the spectrum.
Example 3: Calculate the predicted velocity ratio in Newton’s model for light going from air to glass
(n = 1.5).
v
Solution: Newton predicted: vglass
air
= n = 1.5 Therefore: vglass = 1.5 × vair (This prediction was later
proven incorrect)

12 Advanced Assignment Problems

1. Explain why Newton’s corpuscular theory fails to account for the bright spot in the center of a circular
obstacle’s shadow (Poisson’s spot).
2. Calculate the force required to change a corpuscle’s path when it refracts from air to diamond (n =
2.42) at 45° incidence.

3. Design an experiment that could distinguish between Newton’s corpuscular theory and Huygens’ wave
theory using only 17th-century technology.
4. Analyze how Newton’s theory would predict the behavior of light in a fiber optic cable.
5. Compare the energy requirements for Newton’s corpuscular emission versus modern photon emission
from atomic transitions.
6. Derive the relationship between corpuscle size and refractive index according to Newton’s model.
7. Explain how Newton’s attraction/repulsion hypothesis fails for total internal reflection.

13 Historical Impact and Modern Perspective

Newton’s corpuscular theory, despite its flaws, established crucial principles:
• Quantitative approach to optics

• Particle nature concepts later validated in quantum mechanics

• Mathematical framework for ray optics
• Foundation for understanding light-matter interactions
The theory’s 18th-century dominance demonstrates the importance of experimental verification and the
evolution of scientific understanding[10][12].

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14 References
• Newton’s Corpuscular Theory: Merits and Drawbacks[1]
• Florida State University: Sir Isaac Newton Timeline[2]
• Wikipedia: Double-slit experiment[3]
• Wikipedia: Isaac Newton - Optics[5]

• SATHEE: Young’s Double Slit Experiment[6]

• SlideShare: Newton’s Particle Theory[7]
• Britannica: Isaac Newton Biography[8]

• Britannica: Corpuscular theory of light[10]

• Wikipedia: Corpuscular theory of light[12]