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Understanding the Inverse Square Law
Reading Time: 12 - 15 minutes (3428 words)

Ok, the title of this is almost pure click bait, but keep reading to understand why the grow lights you might be using for you indoor plants or seedlings aren't delivering the amount of light you need and what you can do about it.

The Essentials of Grow Lights in Indoor Gardening

Sunlight streaming in window onto plants

If you've been following the Unlikely Gardener for any length of time then you are probably already well-acquainted with the concept of grow lights — the artificial suns that fuel our plants' growth where natural light is scarce. These artificial sources of light are not just supplements; they are the heartbeats of our indoor gardens, enabling us to cultivate a wide array of plant life within the confines of our homes and offices. Among the spectrum of options available, LED grow lights have surged to the forefront, celebrated for their energy efficiency, longevity, and the spectrum of light they offer, tailored to our plants' photosynthetic needs.

However, even with this advanced technology at our fingertips, we encounter a fundamental challenge that can make or break the success of our indoor gardening ventures: the critical role of light intensity. Light intensity is not just a matter of brightness; it's a vital ingredient for photosynthesis, the very process that empowers plants to convert light into life. But here lies the rub: not all light that shines is absorbed. Thanks to a principle known as the inverse square law, the distance between your plants and their light source can dramatically affect the amount of usable light they receive, with intensity diminishing exponentially as distance increases.

Grow light shining on a ZZ Plant

This phenomenon isn't merely a curiosity of physics; it's a crucial factor that demands our attention and understanding if we are to master the art of indoor gardening. The inverse square law presents a particular challenge for those of us relying on LED grow lights, which, despite their many benefits, often have lower power outputs compared to older grow light systems. The implications of this law mean that without strategic management and thoughtful placement of our lights, we might not be delivering the life-giving luminescence our plants need to thrive.

Thus, the core focus of this unlikely article digs into the heart of this challenge. We hope to demystify the inverse square law and its impact on light intensity from LED grow lights. This post will not only illuminate the physics behind this principle but also arm you with practical strategies to ensure that every photon counts towards the health and productivity of your indoor garden.

Let's get started!

Understanding a Fundamental Difference of Light

Before we get too far down the rabbit hole we have to cover one critical aspect of light that really messes with people's concepts and perceptions; Plants and People see and respond to different wavelengths of light.

Plant with sunglasses

What humans see for our maximum spectral sensitivity under daylight conditions peaks at 550nm, and although we can differentiate between light across the spectrum from 400nm to 700nm, we really get most of our brightness reference in this middle area. When you look a the following graph that compares relative photosynthetic efficiency for plants to the relative spectral sensitivity of the human eye you can get a visual idea of why our perception of what a plant sees as usable light is very different than what we see. There is some overlap but the human peak of sensitivity is at a low point for plants.

Plants have their highest photosynthetic efficiency with blue light with a nearly 100% response rate at the 440nm level, and over 90% within the red spectrum around 680nm. Where humans are most sensitive, and where lumen weighting is highest for us is around 550nm, but at that point for plants, their photosynthetic response is only at about 27%.

Looking at the graph above you can get an idea why any grow lights which list their lumen output (yellow line), and omits any references to how much light is output is available in the photosynthetically active radiation (PAR) ranges are pretty much trying to avoid giving you critical metrics that directly affect your plants. A light can easily deliver "full spectrum" light and at the same time not be useful for your plants.

Deep Dive into Light Intensity and Plant Growth

Introduction to Light Intensity in Indoor Gardening

As you probably already know, for all plant care and gardening, light plays the starring role. It's the catalyst for photosynthesis, where plants convert light, carbon dioxide, and water into glucose—a vital source of energy—and oxygen, a byproduct that enriches our air. As shown above, this process doesn't just happen in any light; it requires the right wavelength and the right intensity to kickstart and sustain it. Without adequate light, photosynthesis cannot proceed efficiently, leading to stunted growth, poor health, and diminished yields. This is where understanding light intensity becomes crucial for any indoor gardener aiming to cultivate thriving plants.

The Essence of Light for Photosynthesis

Photosynthesis is not merely a function of light presence (sorry this is probably sounding kind of repetitive, but it needs to be driving in with a sledgehammer for some); it's a matter of light quality (light-waves measured in nano meters, nm) and quantity (light-particles; PPF/PPFD). Plants have evolved to use specific light wavelengths effectively (blue and red mostly), but the intensity of that light can be the difference between a plant merely surviving and one that's flourishing. Light intensity refers to the brightness level of light that reaches the plant's surface, measured in micromoles per square meter per second (μmol/m²/s, often listed as PPDF). In an indoor setting, mimicking the optimal light conditions for photosynthesis means understanding and managing this intensity to match the needs of our plants.

Why Light Intensity Matters

Light intensity touches every aspect of a plant's life cycle, from the sprout breaking through the soil to the unfolding of leaves and blossoming of flowers. During germination, adequate light intensity encourages strong, healthy seedling growth. As plants enter the vegetative stage, light intensity drives the development of leaves and stems, building a robust framework for future flowering and fruit production. And when it's time for flowering, the intensity of light can influence not just the timing but the quality of blooms and fruits.

High light intensity promotes dense, compact growth, essential for many vegetative or flowering plants and vegetables that require strong light to produce blooms and fruits. Conversely, low light intensity can lead to elongated, weak stems and sparse foliage, as plants stretch toward any available light source. This stretching, or etiolation, not only compromises the plant's appearance but its overall health and productivity.

Understanding and controlling light intensity in an indoor setting allows us to create conditions where plants can perform photosynthesis optimally. By doing so, we ensure our plants have the energy to grow, reproduce, and contribute 9very little) to the air quality in our home and office environments. It's a delicate balance, but one that can be mastered with knowledge and attention to the light needs of different plants. Whether you're nurturing delicate herbs or robust flowering plants, appreciating the critical role of light intensity is your first step towards ensuring their health, beauty, and bounty.

Understanding the Needs of Your Plants

As we dig deeper into the topic of indoor plant care, it becomes evident that the plant kingdom is a tapestry of diversity, woven through with threads of varying needs and preferences. This diversity extends prominently to how plants interact with light — the very energy source that drives their growth. Throughout the eons, plants have evolved under a wide range of light conditions, from the dappled shadows of dense forests to the relentless sun of arid deserts. As a result, each species has developed unique requirements for light intensity, which, if met, lead to optimal growth, health, and productivity.

Diverse Needs Across the Plant Kingdom

To truly master the unlikely art of indoor plant care, we must first acknowledge and respect these diverse light needs. Just as a cactus thrives in the blazing sun, a fern unfolds its fronds in the cool understory of a rain forest, illustrating the spectrum of light environments that plants call home. This variance is not merely a matter of preference but a fundamental aspect of their biological evolution, influencing not only their growth but also their ability to photosynthesize, flower, and fruit. Understanding this diversity is the first step towards creating an indoor space that mirrors the complexity and richness of nature itself.

Categorizing Plants by Light Needs

Recognizing the vast array of light requirements among plants, unlikely gardeners can benefit from categorizing their vegetative babies based on their light intensity needs. This general categorization serves as a guide, helping to streamline the selection and arrangement of grow lights in a way that mirrors the natural world as closely as possible. Keep the 200 - 300 μmol/m2/s top of mind because many/most indoor plants reach their maximum photosynthesis between these levels.

  • Low-Light Tolerant Plants (100 - 200 μmol/m2/s): These plants have adapted to thrive in minimal light conditions, much like the understory plants of a dense forest. They are the ideal choice for spaces with limited natural light, requiring only gentle artificial illumination to do well.
  • Medium-Light Requiring Plants (200 - 300 μmol/m2/s): Occupying the middle ground, this is where the majority of indoor plants do best. These plants require a medium level of light intensity — not too dim, yet not too bright. They are regularly referred to as receiving "bright indirect light", embodying the balance found in nature's more varied environments.
  • High-Light Plants (300 - 500 μmol/m2/s): These are the sun worshipers of the plant world, thriving under bright, indirect and direct light. Mimicking the open, sun-drenched habitats they originate from, high-light plants demand robust illumination. For a human this would typically be where we would start thinking about wearing our sunglasses to reduce eye-strain.

For some additional context, full sun outdoors with no cloud cover is going to deliver between 2,000 and 2,200 μmol/m2/s, and an overcast day at noon would typically deliver in the range of 300 - 400 μmol/m2/s. Full shade on a sunny afternoon would usually deliver around 500 μmol/m2/s which is also about what a 75% shade cloth delivers outdoors on a patio on in a greenhouse.

By categorizing plants according to their light intensity needs, unlikely gardeners can more effectively plan their indoor plant spaces, ensuring each plant receives the level of light it naturally desires. This considered approach not only optimizes plant health and growth but also brings us closer to replicating the diverse and dynamic light conditions found in nature, right within our own homes.

The Inverse Square Law Explained

Unraveling the Mystery of Light Dispersion

Inverse Square Law

At the heart of understanding how light behaves in our indoor spaces lies a fundamental principle of physics known as the inverse square law. This law might sound complex, but it governs a simple truth about light: as it travels from its source, the intensity of light decreases exponentially with distance.

We don't think a lot about this when we think of sunlight because everything on earth is essentially at a fixed distance from the sun. But when it comes to something like a flashlight, our car's headlights, or the grow lights we have in our living room, we need to pay closer attention because it it very important.

The Mathematical Essence

Mathematically, the inverse square law is expressed as I = P/(4πr2) where:

  • I represents the intensity of light,
  • P is the power of the light source (in watts),
  • r is the distance from the light source to the point of interest (in meters),
  • and 4πr2 corresponds to the surface area of a sphere.

In simpler terms, this formula tells us that the light intensity at a certain distance from the source is inversely proportional to the square of that distance. Therefore, if you double the distance from a light source, the light intensity at that new point is not merely halved; it's reduced to one-fourth of its original intensity.

Visualizing the Inverse Square Law

Imagine a light source in the center of a dark room. As this light travels outward, it spreads over a larger area, diluting its intensity. At one meter away, the light might be bright and focused. Move two meters away, and the brightness noticeably dims, not just by half but significantly more. This effect is not a linear decrease; it's exponential, meaning the farther you are, the more dramatic the drop in light intensity.

Practical Implications for Indoor Plant Care

For all of us indoor plant parents, this principle has profound implications. Using LED grow lights, while efficient and eco-friendly, requires an understanding to placement and distance. A common challenge arises when trying to ensure plants receive sufficient light. Placing a suitably powerful grow light too far from your plants can result in inadequate light intensity, impacting plant growth, health, and overall photosynthetic potential. Conversely, placing lights too close might risk light burn or excessive heat exposure for certain plants.

Compounding the physics issue is the fact that not only are human eyes more responsive to different frequencies as we detailed earlier in this post, but they adapts via our iris to let more or less light in to better help us see in varying light conditions. What we perceive is continually adapting to better help us.

To navigate these challenges, understanding the inverse square law is crucial. It guides us in positioning our grow lights at an optimal distance, ensuring that our plants receive the right amount of light without waste or harm. This balance is key to cultivating a thriving indoor plant collection.

Challenges Posed by the Inverse Square Law for LED Grow Lights

When we venture into the world of indoor plant care, particularly with the aid of LED grow lights, we're not just growing plants; we're engineering environments. A pivotal factor in this delicate balancing act is understanding the inverse square law and its implications for our planty friends. This law that we've already detailed, a scientific principle as unforgiving as gravity, dictates that the intensity of light from a source (our trusted LED grow lights, or any other light source) diminishes exponentially with distance. For those using low-powered LED lights, this presents a series of challenges that, if not navigated wisely, can lead to less-than-ideal outcomes for plant health and productivity.

The Reality of Inexpensive Grow Lights

At its core, we should all all now understand the inverse square law which, as we've detailed, tells us that the intensity of light is inversely proportional to the square of the distance from the source. In kindergarten simplicity, if you double the distance between your plant and the light source, the plant receives only a quarter (25%) of the light intensity.

This principle is particularly pertinent when considering the purchase and use of inexpensive LED grow lights. These lights, which are often very low intensity to start with, have their value further reduced as their distance is increased, often for the purpose of illuminating more plants.

Real-World Impacts for Our Plants

With this in mind, consider a common scenario for the typical indoor plant collection: a living room setup and illuminated with LED grow lights aimed at nurturing a variety of plants, from shade-tolerant ferns to light-loving tomatoes, and full-sun succulents. In an ideal world, each plant would receive its precise light requirement without a hitch. However, the inverse square law introduces a complexity, particularly for those low-powered LEDs.

Example 1: The Leggy Seedling Dilemma

A classic example of the law's impact is observed in seedlings grown under LED lights positioned too high above them. In an effort to ensure coverage for all, the distance inadvertently results in significantly reduced light intensity reaching the young plants. The outcome? Leggy, stretched seedlings straining towards a light that, by the law of physics, is failing to deliver the intensity they crave. This scenario underscores the delicate dance of positioning — too far, and the plants suffer; too close, and you risk other complications. This usually includes all grow lights that output less than 50 μmol/m2/s which, while great for new emerging seedlings fail as soon a the plants get their first true leaves.

Example 2: The Uneven Canopy Challenge

Another illustration is the plight for cultivating a mixed canopy under a singular LED grow light. The plants positioned directly beneath the light revel in its intensity, while those on the periphery languish in the shadows of an exponential drop-off in light. The result is an unevenly grown canopy, with plants at the edges struggling to match the vigour of their centrally located counterparts. This spatial dilemma highlights the inverse square law's indiscriminate nature, affecting plant growth and yield across the board. This affects all lights, but most often is most apparent with the single or double row LEDs in the 50-100 μmol/m2/s range where the angle of light beam is 120° or so. The minimal volume of light is spread so far apart that the only area of intensity on consistent level is an inch or two wide, and directly under the light fixture. Move outwards from there, and across an uneven foliage and light intensity drops dramatically. This is most apparent with the multi-head flexible clamp on lights which are often placed at odd angled which only reduces the concentrated light zone.

With the included example, but it applies to all manufacturers, keep in mind that most vegetative plants photosynthesize best between 200 and 300 μmol/m2/s. At a 10" distance away from your plants' foliage the Barrina light intensity is already at the lower limit. The numbers shown in this image are the best case light intensity readings under the "hottest" area, which is a very small part of the total coverage area.

Navigating the Challenge

The inverse square law might seem like a formidable opponent, but awareness and strategic planning can turn the tides. By understanding the spatial dynamics of light distribution, unlikely gardeners can select better grow lights for their environment, better position their LED grow lights to maximize light intensity, adjust their plant groupings for better light consistency, and even use reflective materials to reduce some of the law's effects. The goal is to create a uniformly lit environment that caters to the needs of all plants, ensuring that each receives its share of light for optimal growth and productivity.

The bottom line: Low output (sub 150 μmol/m2/s), typically inexpensive grow lights, while seemingly able to increase the brightness of your planting area, often aren't able to deliver a level of light that meets the minimum photosynthetic needs of many plants beyond seed starts and veggie seedlings.

This does not mean they are completely without value, but it does mean that you need to use and position them in a way that increases the light intensity for the plants you are hoping to energize, in almost every case this requires that the lights be moved closer to a plant and plant canopy, this in turn means that a smaller area is illuminated, which then means more lights are required to provide adequate light coverage for all your plants.

Light intensity isn't cumulative unless it overlaps so using two 50PPFD lights does not mean 100PPFD is achieved, it often means that the plant(s) simply get more even coverage of 50PPFD light. For a plant to get 100 μmol/m2/s, both light cones from both lights would have to shine on the entire plant, across the same area.

Plants in the wild get more even and equal coverage as the sun traverses the sky from East to West, and the distance is always effectively equal, at roughly 92,416,537.42 miles. While we can't manipulate direct sunlight, reflected light does fall victim to the Inverse Square Law with the point source being the reflected surface it hits. At this point we get into all sorts of other complicated light calculations related to ray tracing, dispersion patterns, and reflective densities, but this is often why many plants are said to be able to tolerate "indirect" light. Essentially, indirect light is what we often refer to as ambient light, and all of it comes from a reflected source.

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