In point by point calculations what we’re trying to do is find out exactly how much light the light levels are in a very given point. To do this we use one of my absolute favorite math equations, the inverse square law. Every lighting practitioner should have this memorized. The good news it is very simple. E which stands for luminance is equal to CP over D-squared, candlepower over D-squared. when light is pit perpendicular to the surface in order to find out how many foot candles we have, we measure the intensity, the candlepower at this given point and we divide it by the distance squared. Let’s have an example, if we have a 10 degree spot it has an 11,500 candlepower at six feet away. 6 is the distance, the intensity is 11,500. 11,500 divided by six squared equals 319,4 fc. When we’re hitting light on a not flat surface we’re hitting it at more than angle, we have to use the cosine law. Let me try to explain this. The light intensity doesn’t change but the angle in which it’s hitting someone or hitting the surface, that’s going to change. Why do I say someone? It’s a lot like any collision sports such as football or hockey. If an individual is coming to hit another player, What happens is that power, if you’re hit dead on, hits with full brunt force. But what happens is, The individual who is going to get hit tries to move a little and changes the angle of the surface. In doing so it diminishes the effect. However, the person is still coming with exactly the same intensity as if he had hit him straight on. We use this as a cosine law. Here’s an example of it. So what we do is we would use what’s called a Candela Distribution Curve. These distribution curves show us the light intensity at any given angle. If we know what the late intensity is any given angle and we know how the far the distance is, we can quite simply just find out how many foot candles will arrive at that place. The other way that it works the way that I love how it works, is that we won’t have to pick and choose which luminaire will do the job. If we have a twenty five foot high ceiling with a work cavity of twenty feet, so we’re trying to throw the light 20 feet to our work plain and we require 50 foot candles at the horizontal task. What I can do is I can use this inverse square law change it around a little and find out how many candlepower is required to start. Let’s use this as an example. If E is equal to CP over D squared therefore CP is equal to E multiplied by D-squared. CP if we’re at fifty foot candles is fifty, 20, twenty times twenty is 400, fifty times 400 is 20,000. We need to look for a luminaire that has about 20,000 candlepower. That is the digest of a inverse square law and that is why it’s one of my favorite equations. Now we’re going to show how the inverse square law works. We’ve got an LED PAR lamp with the center beam candlepower a 4800 candlepower or Candela. We’re going to be four feet away from the lamp. We measure and we get practically 300 foot candles which is perfect. Now when I take my light meter and I move it from four feet to two feet, I’m halving the distance, so it should be twice as strong. However I now have 1200 foot candles, four times. This is the inverse square law. Now let’s illustrate the cosine law. We have our same fixture here, our same lamp with the same candlepower and its hitting perpendicular to this surface, but what happens when I take this and I angle it and I give it and angle? Notice that the beam covers a greater area. So therefore I have less light in one specific part, and that’s where we use the cosine law.