How Far Can Light 'Feel' a Boundary?

A Plain-Language Explanation of Transverse Sensitivity

David Allen LaPoint

Primerfield Foundation

What This Paper Is About

When light passes near the edge of an object — like a razor blade or the edge of a doorway — something interesting happens. The light doesn't just travel in a straight line past the edge. Instead, the presence of that edge affects where photons (particles of light) end up being detected, even when the detector isn't directly behind the edge.

This paper answers a simple but important question: How far sideways from an edge can light still be affected by that edge?

The answer turns out to be surprisingly large — for visible light, the influence of a boundary extends several millimeters sideways. That's thousands of times larger than the wavelength of the light itself.

What Do We Mean by 'Sensitivity'?

Imagine you're standing near a wall, and someone is shining a flashlight from the other side. If you move sideways, at some point the wall no longer affects whether the light reaches you. But how far do you have to move before the wall's presence stops mattering?

That's essentially what we're measuring here — but at a much smaller scale, with individual photons of light passing near sharp edges.

Key definition: The "transverse sensitivity distance" is the sideways distance from an edge beyond which all remaining intensity variations stay within 5% of the unobstructed (normal) intensity. This is the point where the edge no longer has a significant effect on where photons are detected.

The word "transverse" simply means "sideways" — perpendicular to the direction the light is traveling.

Why Is This Tricky to Measure?

Here's the complication: when light passes an edge, the intensity doesn't smoothly settle down to its final value. Instead, it oscillates — going slightly above and below the expected value repeatedly before finally stabilizing.

Think of it like a guitar string that's been plucked. It doesn't immediately stop at its resting position — it vibrates back and forth, with the vibrations gradually getting smaller until the string is still.

Because of this oscillating behavior, you can't just ask "where does the intensity first reach normal?" because it crosses the normal level many times. Instead, this paper uses an "envelope" approach: we ask "beyond what distance do ALL the remaining oscillations stay within 5% of normal for all farther positions?"

The Key Finding

For visible light (the kind we see with our eyes) traveling about 20 centimeters (8 inches) before being detected:

The boundary influence extends about 2 millimeters sideways.

This might not sound like much, but consider this: visible light has wavelengths measured in nanometers (billionths of a meter). A wavelength of green light is about 500 nanometers, or 0.0005 millimeters. So 2 millimeters represents about 4,000 wavelengths!

In other words, the "reach" of a boundary extends thousands of times farther than the wavelength of the light itself.

How the Sensitivity Distance Depends on Color

Different colors of light have different wavelengths. Red light has longer wavelengths (around 700 nanometers) while violet light has shorter wavelengths (around 400 nanometers). The chart below shows how the sensitivity distance changes with wavelength.

Chart showing sideways distance affected by an edge vs wavelength of light

What this chart shows: As the wavelength gets longer (moving from violet toward red), the sideways distance affected by a boundary increases. Red light (700 nm) is affected about 2.4 mm from a boundary, while violet light (400 nm) is affected only about 1.8 mm away. The relationship follows a square-root pattern — double the wavelength, and the distance increases by about 40%.

The Same Data, Measured in Wavelengths

Another way to look at this is to ask: how many wavelengths does this distance represent? This gives us a sense of scale that's independent of the specific units we use.

Chart showing sideways influence measured in number of wavelengths

What this chart shows: When we express the sensitivity distance in terms of wavelengths rather than millimeters, we see that shorter wavelengths (violet) actually span MORE wavelengths (about 4,500) than longer wavelengths (red, about 3,400). But in either case, we're talking about THOUSANDS of wavelengths — a remarkably large number. This means the influence of a boundary extends far beyond what you might naively expect from the size of a single wave cycle.

How Travel Distance Affects the Sensitivity

The sensitivity distance also depends on how far the light travels after passing the edge before being detected. The farther the light travels, the larger the sideways region that gets affected.

Distance traveled	Sensitivity distance
2 cm (less than 1 inch)	0.64 mm
20 cm (about 8 inches)	2.0 mm
2 meters (about 6.5 feet)	6.4 mm
20 meters (about 65 feet)	20 mm (about 3/4 inch)

What this table shows: The sensitivity distance grows with the square root of the travel distance. If you increase the travel distance by a factor of 100 (from 2 cm to 2 meters), the sensitivity distance increases by a factor of 10 (from 0.64 mm to 6.4 mm). This means the numerical value of the sensitivity distance depends on the experimental geometry, while the underlying scaling behavior follows standard Fresnel diffraction.

What This Does NOT Mean

It's important to be clear about what these results do and don't tell us:

This does NOT define a 'size' of a photon
This does NOT mean there's a force reaching out from the photon
This does NOT mean information is traveling sideways across the sensitivity distance
This does NOT commit to any specific explanation for WHY this happens

What we've done is simply quantify HOW FAR the influence extends (using standard Fresnel diffraction predictions), not explain the mechanism behind it. The results are compatible with multiple different physical explanations.

Different Types of Experiments

This paper looks at three classic experiments involving light and edges:

1. Edge diffraction (knife-edge): Light passing by a single sharp edge, like a razor blade. This is the main focus of the paper and gives the clearest measurement of the sensitivity distance.

2. Single-slit diffraction: Light passing through a narrow opening. Here there are two edges (both sides of the slit), and the paper shows that the edge results give a useful rule of thumb: for visible light at similar propagation distances and using the same 5% criterion, if the slit is wider than about 4 mm, the center of the slit is essentially unaffected by either edge.

3. Double-slit interference: Light passing through two narrow slits and creating an interference pattern. This experiment is actually measuring something different — it depends on how "coherent" the light source is, not just on edge proximity. So the sensitivity distance concept from edge experiments doesn't directly apply here.

The Bottom Line

When light passes near a boundary, that boundary affects the light's behavior over a surprisingly large sideways distance — typically a few millimeters for visible light in a tabletop setup. This distance:

Increases with wavelength (red light is affected over a larger area than violet)
Increases with travel distance (the farther the light goes, the larger the affected area)
Spans thousands of wavelengths (not just one or two)
Depends on the geometry of the experiment, not just the light itself

This paper establishes these facts as clear, quantitative constraints under a consistent operational definition. Any theory intended to reproduce standard Fresnel edge-diffraction behavior in this geometry must be able to reproduce these quantitative results.

Why Does This Matter?

Understanding the spatial scale over which boundaries affect light is important for:

Designing optical instruments and experiments
Understanding the fundamental behavior of photons
Testing theories about the nature of light

By putting specific numbers on this effect — rather than just saying "light diffracts near edges" — we create a concrete benchmark that can be used to evaluate different physical models of how light works.

A Note on Interpretation

This paper deliberately avoids saying WHY this sensitivity distance exists. It simply documents WHAT the distance is and HOW it scales with wavelength and geometry. This approach allows the results to be useful regardless of which theoretical framework you prefer for understanding light.

Whatever framework you prefer for understanding light — whether waves, particles, fields, or something else — any model intended to reproduce standard single-photon, linear-optics Fresnel diffraction statistics in this geometry must match these sensitivity distances under the stated definition.