Transverse Sensitivity Scale of Photons

Inferred from Classical Diffraction Experiments

David Allen LaPoint

PrimerField Foundation

January 2, 2026

Abstract

When light passes near an edge or through a slit, it bends in predictable ways. This bending is called diffraction. Scientists have long known how to calculate diffraction patterns, but a simpler question is often overlooked: how far from an edge does the light "notice" that the edge is there? This paper answers that question using well-established physics. For visible light traveling about 8 inches (20 cm) before hitting a detector, the answer is roughly 2 millimeters—about the thickness of a nickel. This distance spans thousands of wavelengths of light. These results come directly from standard physics equations that have been tested countless times. We make no claims about why light behaves this way—only that any complete explanation must account for these observed diffraction statistics under the stated geometry.

1. Introduction

When light passes by an edge—like the edge of a razor blade—it doesn't just travel in a straight line. It bends slightly around the edge, creating patterns of bright and dark bands. This behavior, called diffraction, has been studied for over 200 years. Scientists can predict these patterns with remarkable accuracy.

But here's a question that's often overlooked: if you're standing some distance from the edge (on the lit side), how far away can you be before the edge stops affecting where light lands? In other words, over what distance does the presence of an edge change the measured landing pattern of light?

This paper answers that question directly. We use the same well-tested equations that physicists have relied on for centuries. Our contribution is simply to state the answer clearly in everyday units—millimeters rather than abstract mathematical coordinates.

An important note on language: when we say the edge "influences" light over a certain distance, we mean only that the statistical pattern of where photons land differs from what it would be without the edge. We are not claiming the edge exerts a force, that light has a physical size, or that information travels across this distance. We're simply describing what the math tells us about where light lands.

2. Setup and Definitions

2.1 The Basic Setup

To make our results easy to compare, we use the same setup throughout: green light (wavelength 500 nanometers, or 500 billionths of a meter), traveling 20 centimeters (about 8 inches) from the diffracting edge to a detector. We also work with very dim light—so dim that individual photons (particles of light) arrive one at a time. Over many photons, the familiar diffraction pattern emerges.

2.2 The Fresnel Length: A Natural Measuring Stick

When physicists study diffraction, they use a natural length scale called the Fresnel length. Think of it as a built-in measuring stick that depends on the wavelength of light and how far the light travels. The formula is:

w = √(λz/2)

where λ (lambda) is the wavelength and z is the travel distance. For our setup (green light, 20 cm travel), this works out to about 0.224 mm—roughly a quarter of a millimeter.

2.3 Defining "Close Enough to Normal"

Here's a complication: as you move away from an edge, the light intensity doesn't smoothly approach its normal value. Instead, it wobbles—overshooting, then undershooting, then overshooting again, with the wobbles gradually shrinking.

Because of this wobbling, we can't simply ask "where does the intensity equal normal?"—it crosses that value many times. Instead, we ask: "How far away must you be before the wobbles stay within 5% of normal?" This gives us a clear, reproducible answer.

The 5% threshold is a practical choice—strict enough to be meaningful, but not so strict that the answer becomes impractically large.

3. Edge Diffraction (The Knife-Edge Case)

3.1 The Math

The simplest diffraction case is a straight edge—imagine a razor blade blocking half the light. The mathematical formula for the resulting pattern involves what are called Fresnel integrals. These are well-understood functions that can be calculated precisely.

3.2 What the Numbers Show

Table 1 shows how the light intensity varies as you move away from the geometric edge (the point where you'd expect the shadow to end if light traveled in perfectly straight lines). Notice how the intensity wobbles—sometimes above normal, sometimes below.

Table 1. Light intensity at various distances from the edge.

Distance from Edge	Intensity	Deviation	Actual Distance
3 Fresnel lengths	110.8%	10.8%	0.67 mm
5 Fresnel lengths	106.5%	6.5%	1.12 mm
8 Fresnel lengths	96.1%	3.9%	1.79 mm
10 Fresnel lengths	96.9%	3.1%	2.24 mm
15 Fresnel lengths	102.1%	2.1%	3.35 mm
20 Fresnel lengths	98.4%	1.6%	4.47 mm
30 Fresnel lengths	98.9%	1.1%	6.71 mm
50 Fresnel lengths	99.4%	0.6%	11.18 mm

3.3 Finding the Sensitivity Distance

Using our 5% threshold (wobbles must stay within 5% of normal), the edge's influence extends about 9 Fresnel lengths. For our setup, that's approximately 2.0 mm—about the thickness of a nickel, or roughly 4,000 wavelengths of green light.

Table 2 shows how this distance changes with different thresholds. A stricter threshold (smaller percentage) requires a larger distance.

Table 2. Sensitivity distances for different strictness levels.

Threshold	Fresnel Lengths	Actual Distance
10% (loose)	~4.4	~1.0 mm
5% (standard)	~9.0	~2.0 mm
3%	~15.0	~3.4 mm
2%	~22.6	~5.1 mm
1% (strict)	~45.1	~10.1 mm

3.4 Different Colors of Light

The sensitivity distance depends on wavelength. Longer wavelengths (red light) have larger sensitivity distances than shorter wavelengths (violet light). Table 3 shows this relationship.

Table 3. Sensitivity distances for different colors of visible light (5% threshold, 20 cm travel distance).

Color	Wavelength	Sensitivity Distance
Violet	400 nm	1.8 mm
Blue	450 nm	1.9 mm
Green	500 nm	2.0 mm
Yellow	580 nm	2.2 mm
Red	700 nm	2.4 mm

3.5 A Striking Observation

Perhaps the most surprising result is how many wavelengths fit within the sensitivity distance. For visible light in our setup, the edge influences light over 3,400 to 4,500 wavelengths—thousands of times larger than the wavelength itself.

4. Single-Slit Diffraction

4.1 Two Edges Instead of One

A slit has two edges, and both affect the light passing through. The math is more complicated than for a single edge, but our edge results give a useful rule of thumb.

4.2 A Practical Guideline

For the center of the slit to be relatively free of edge effects, the slit should be at least twice the sensitivity distance—about 4 mm wide for our setup. Narrower slits will show stronger diffraction effects at their center.

5. Double-Slit Interference

5.1 A Different Phenomenon

The famous double-slit experiment—where light passing through two slits creates an interference pattern—works differently from the edge diffraction we've been discussing. The key factor isn't distance from the edges; it's how "coherent" the light source is.

5.2 Coherence Width

A well-prepared light source (like a laser) can maintain coherence over centimeters—far larger than our edge-diffraction sensitivity distance. The two phenomena are governed by different physics.

5.3 Why Our Method Doesn't Apply

Our envelope-based approach—looking for when intensity settles to within 5% of normal—doesn't work for double-slit interference. The relevant quantity there is "fringe visibility" (how sharp the stripes are), not intensity deviation. So we cannot extract a sensitivity distance from double-slit experiments using our method.

6. How Travel Distance Affects the Results

So far we've used a 20 cm travel distance. But the sensitivity distance depends on how far the light travels before being measured. Longer travel distances give larger sensitivity distances. Table 4 shows this relationship.

Table 4. How sensitivity distance grows with travel distance (green light, 5% threshold).

Travel Distance	Fresnel Length	Sensitivity Distance
2 cm (< 1 inch)	0.071 mm	0.64 mm
20 cm (8 inches)	0.224 mm	2.0 mm
2 m (6.5 feet)	0.707 mm	6.4 mm
20 m (65 feet)	2.236 mm	20.1 mm

This is crucial: the sensitivity distance is not a fixed property of light. It depends on the experimental setup. Move your detector farther away, and the sensitivity distance grows.

7. Discussion

The sensitivity scale we've identified—roughly 2 mm for visible light at 20 cm—is not a new prediction. It's built into the standard Fresnel equations that physicists have used for two centuries. Our contribution is simply to state this scale explicitly and define it precisely.

The wobbling approach to normal intensity explains why we need an envelope-based definition. The intensity doesn't smoothly settle to its final value—it oscillates around it with gradually shrinking amplitude.

We emphasize again: "sensitivity" here means only that the statistical pattern of where photons land changes when edges are within this distance. It does not mean light has a physical size of 2 mm, that edges exert forces over this distance, or that information travels from the edge to the photon.

Any theory that claims to explain diffraction detection statistics in this geometry must reproduce these numbers. The constraints we've stated are: (1) single photons build up diffraction patterns one at a time; (2) detection patterns change when edges are within the sensitivity range; (3) the scale depends on both wavelength and travel distance; (4) the approach to normal is oscillatory, not smooth; and (5) the sensitivity distance spans thousands of wavelengths.

This paper establishes what the measurements show. It does not claim to explain why. Multiple explanations are possible, including models where photons have associated field structures extending over these distances. Any such model must reproduce the constraints documented here.

8. Conclusions

By applying a consistent definition across different diffraction setups, we've extracted a clear answer to a simple question: how far from an edge does light "notice" the edge is there?

For visible light traveling 20 cm, the answer is about 2.0–2.4 mm (depending on color), using a 5% threshold. This spans several thousand wavelengths. The scale grows with both wavelength and travel distance—it's a property of the setup, not of light itself.

Edge and single-slit diffraction give consistent results. Double-slit interference involves different physics and cannot be analyzed the same way.

These results come from standard, well-tested physics equations. We make no claims about why light behaves this way—only that it does, and that any complete theory must account for these facts.

References

[1] M. Born and E. Wolf, Principles of Optics, 7th ed., Cambridge University Press (1999). Chapter 8 covers diffraction theory.

[2] J. W. Goodman, Introduction to Fourier Optics, 3rd ed., Roberts & Company (2005). Chapter 4 covers Fresnel diffraction.

[3] E. Hecht, Optics, 5th ed., Pearson (2017). A standard undergraduate optics textbook.

[4] A. Sommerfeld, Optics: Lectures on Theoretical Physics, Vol. IV, Academic Press (1954).

[5] A. Fresnel, "Mémoire sur la diffraction de la lumière" (1818/1826). The original work on diffraction.

[6] R. P. Feynman, QED: The Strange Theory of Light and Matter, Princeton University Press (1985). An accessible introduction to quantum electrodynamics.

[7] P. Grangier, G. Roger, and A. Aspect, "Experimental evidence for a photon anticorrelation effect," Europhysics Letters 1, 173–179 (1986). Single-photon experiments.

[8] L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press (1995). Chapter 4 covers coherence.

Appendix: Mathematical Details

For readers familiar with calculus, here are the key formulas.

The Fresnel integrals are:

C(u) = ∫₀ᵘ cos(πt²/2) dt

S(u) = ∫₀ᵘ sin(πt²/2) dt

For knife-edge diffraction, the intensity formula is:

I(u)/I₀ = (1/2)[(C(u) + 1/2)² + (S(u) + 1/2)²]

For large distances from the edge, the deviation from normal decays approximately as:

|I/I₀ − 1| ≈ 0.45/u

Setting this equal to 5% (0.05) gives u* ≈ 9.0 Fresnel lengths.

Reproducibility: All calculations can be verified using any standard scientific computing software that includes Fresnel integral functions (such as Python's scipy library).