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Debunking the Inverse Square Law

Forget everything you've learned about the Inverse Square Law - it does NOT apply to focused lighting!

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The Inverse Square Law applies only to light that radiates omni-directionally, not to focused parabolic lighting.

Intro

The Inverse Square Law is a characteristic of energy propagation that is often misrepresented and misunderstood in the context of photography lighting modifiers.  The Law states that the intensity of a source decreases at a ratio inversely proportional to the square of the distance it travels.  Basically this means, as the distance doubles, the light intensity decreases by a factor of 4.   But how does this work exactly?   The Inverse Square Law refers to energy that is radiating uniformly from a source - NOT directionally.  It actually refers to the geometry of a sphere - imagine the light as a sphere of coverage that continues to grow as it travels from the source in all directions.  The surface area of this sphere grows by a factor of 4 as the radius doubles.  The Inverse Square Law does NOT mean that light rays become weaker as they travel - only that the density of the light rays decreases in a given area, because the light is spreading out.

For this reason, it is important to understand is that the Inverse Square Law only applies to omni-directional light.   For example, soft boxes that diffuse the light evenly, or bare bulb strobe sources that emit in all directions, both fall under this category.   Since Parabolic Reflectors focus the light into a directional beam, they do not follow this Law.  When light is collimated, or focused into a straight beam using a parabolic reflector, the Inverse Square Law does not apply, and the light maintains its intensity and vibrance as it travels.  This is often referred to as the "throw of the light", and is key to understanding why a focused Parabolic Reflector maintains its appealing look at greater distances.

Omni-Directional Light

Omni-directional light radiates in all directions from the source.  Think of the emitted light as a sphere that continues to grow in area. In this case, as the distance from the source increases by 2x, the area of the sphere of light grows by 4x (see Image 1/2 above). As a result, the amount of light rays hitting a given area or subject decreases to 1/4 (the inverse square of 2, which is 2 stops of light less). If the subject is placed too far away from the source, this can result in very "dull" looking lighting, because the density of light on the subject decreases so drastically. However, this can also be used to your advantage:  if the light is placed close to the subject, it can be used to create very dramatic and appealing images, since the the light falloff is so extreme.  Generally speaking, the more a light is diffused or omni-directional - like a softbox, white umbrella, or other diffused source -  placing the light closer to the subject will give more appealing results. Each modifier is slightly different, however, so it is important to test where the "sweet spot" is for you.

Focused light

A parabolic reflector is a light collimator - that is, it focuses the light into a straight and narrow beam. In this case, the entire output of the source is directed very efficiently into parallel rays with minimum spread.  Therefore, the density of the light rays - and the intensity of the light - remains much more consistent as the light travels (see Image 2/2 above).  For this reason, the Inverse Square Law does not apply to focused light.    As a result, when using a parabolic reflector in a focused position, the subject can be placed much farther away from the light without loosing the vibrant quality of the light.  We usually refer to light like this as having a long "throw".   Using the Focusing Mount, as you move the light source away from the Focus Position inside the reflector, the light starts to spread out and behave more like an omni-directional source -  gradually, the inverse square law applies when the light is fully flooded. Remember, the more the light spreads out, the closer it should be placed to the subject.   Overall, this is one of the reasons why a Parabolic Reflector is such a versatile light shaper - because it can act as both a focused light, and a diffused light, and everything in between! 

In Practice

In practice, there is always some widening and softening of the light beam even when using a focused parabolic reflector - it is not as precise as a laser (although the concept is the same).   This can actually be considered a benefit in many ways, because it leads to a light that has some inherent softening, which is favorable in photography lighting.  Because of this, the light will have some degree of falloff and spread, but not as much as an omni-directional source.

Summary
  • Forget everything you've learned about the Inverse Square Law from photography blogs - these can be very misleading.

  • Light doesn't mysteriously "die out" as it travels - it either spreads out, or it is absorbed or reflected when it hits an object.

  • If a beam of light spreads outthe density of light rays decreases in a given area (what we interpret as the light loosing its intensity).

  • The Inverse Square Law is a property of spherical geometry, not light!  Omni-directional light fills an every-expanding sphere of coverage as it travels away from the source.  As the distance from the source increases by 2x, the area of this sphere increases by 4x, and therefore the density of light rays in a given area decreases to 1/4 (the inverse square of 2).

  • Focused Parabolic Lighting emits light in collimated (parallel) light rays, therefore the Inverse Square Law does NOT apply.

  • The more focused a light source, the further the "throw" of the light (the light can be placed further away from the subject).

  • The more diffused the light source, the more quickly it looses its measured intensity, and the closer you want to place the light to your subject. 

Further Info

After reading and understanding the above, you can now start to understand why energy collimation is used so often in many scientific fields (satellite dishes, for example) -  to transmit or receive energy to and from very far distances without loosing its intensity.  This applies to light waves, radio waves, radar, sonar, etc.   Another example: a lighthouse uses a focused Fresnel lens to "throw" a light many miles - this is only possible because the light beam is collimated, and therefore does not loose its intensity as it travels.

Click here for more information on the Inverse Square Law, or just Google it!

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