light intensity inverse square law equation

#LIGHT INTENSITY INVERSE SQUARE LAW EQUATION HOW TO#

This drawing is from the Wikipedia topic. Our light remains the same as it travels (the photons don't lose energy), but as it spreads out, the light density per unit area is diluted. The Inverse Square Law is only saying that the light spreads to cover a larger area as it travels further, which dilutes it, so to speak.

And at triple the distance, the coverage dimensions triple, both width and height, so the lighted area becomes 9x larger (the square of 3), and the same light there is 1/9 as bright. The drawing explains why it falls off so fast. At twice the distance, each of the width and height dimensions do become doubled, but the area is width x height, which is 4x, and the same light is 1/4 brightness in it. Our eye sees an area, and so Luminance is light per unit area. We might imagine that if the light were twice as far away, it would be half as bright, but the correct answer is only 1/4 as bright. All light spreads and weakens this way, your flashlight, the street light, your table lamp, and your photo flash, all spread and weaken in this way too, with distance. Think of a handheld flashlight, same thing - as the beam travels farther away from the source, the beam spreads out to illuminate a larger area, but becoming more dim with distance. I did not do that experiment.Inverse Square Law is just a fancy name for a rather simple concept. In this case, the field varies inversely by the square of distance. In the website above, the professor also tests a long bar magnet. The average of the values of m is 3.05, indicating that as the magnet gets farther away, the exponent m is about -3, indicating that for this type of magnet only, the force from its magnet field varies inversely by the cube of distance.

A really important point: the compass could detect magnet field at 356 mm, over seven inches away. The table shows the relationshio between magnetic force and distance, as measured by the compass needle deflection method. After doing this test a few times and taking the average, the results are shown in the table below. You measure compass needle deflection at different distances, then find the exponent for the relationship using trig formulas provided.

#LIGHT INTENSITY INVERSE SQUARE LAW EQUATION HOW TO#

After more Googleing, I found a great website describing how to measure magnetic field using an ordinary compass. My tests were inconclusive, after all the distance I could detect with my device only went to 18 mm. Distance from magnet, mm Dīut the table only goes af far as my scale could detect force from the magnet, only about 18 mm, less than an inch! The table shows the relationship between magnetic force and distance, as measured in my test on the saw table. At closer distances the exponent kept decreasing, getting close to zero. I 'guessed' that if my testing device was sensitive enough, the exponent would approach -3, which would indicate inverse cube law.

As the magnet gets farther way from the saw table, the exponent gets larger, and is about -2.5 at 18.26 mm.

So only at a distance of about 16 mm does the magnetic field follow the inverse square law (exponent = -2). x^m = y m Log x = Log y m = Log y / Log x The table shows exponent m for distances of 1.28 mm (almost touching the saw table) to 18.26 mm (magnet force barely detectable). In the following equation, I needed to find exponent 'm'. Since I was looking for an exponent (the exponent is -2 for an inverse square relationship) I decided to analyze the raw Excel data. I went back to my math books to find a solution.

Light intensity inverse square law equation