The light intensity curves for LEDs, regardless of whether they are collimated with a lens or reflectors, follow a bell shaped curve (often referred to as a 'Lambertian' curve). The 50% intensity point for an LED with no optic (bare LED) is virtually always at approximately 120 degrees (60 degrees in each direction).
The 50% point (known as the “beam angle” or “viewing angle”) is a lesser number of degrees depending on the collimating specification used. The beam angle is the total angle in both plus and minus directions.
What is not commonly known by those not experienced in the physics of LED light emission and optics is that the Lambertian LED light intensity curves can be very misleading in terms of how much light is actually arriving at the receiving end.
The emitted light travels in a straight line whose length varies as the angle increases. A beam of LED light traveling at an angle of 45 degrees from straight ahead is at a diagonal, which is the hypotenuse of that 45-degree angle. That is, the light must travel 1.414 farther to reach its destination. For angles greater or less than 45 degrees, that diagonal distance is more or less.
Furthermore, it should be noted that light intensity (just like radio and sound waves) decreases inversely as the square of the distance. This characteristic is known as the “inverse square law.” That means that the light traveling diagonally, per a 45 degree shift to the left or right decreases by 1.0/1.4 × 1.4 or 1/1.96 = 1/2 if rounded off. The result is that the intensity of the LED beam of light, traveling at a 45-degree angle toward a wall, is reduced by 50% from what it would be if just traveling straight ahead at zero degrees.
Consequently, when one looks at a Lambertian LED intensity curve, or a “polar intensity plot” one must divide any value by