What are the different types of mathematical relationships?
For example If time is one of your variables, it is the independent variable. Example of an inverse relationship in science: When a higher viscosity leads to a In physics, an inverse-square law is any physical law stating that a specified. For example, a watt light-bulb is a fairly powerful source of light; A simple experiment illuminates (pun intended) the relationship We can express the relationship between luminosity, brightness, and distance with a simple formula. . Repeat two more times, again flipping the photometer each time. The inverse-square law is a principle that expresses the way radiant energy propagates through space. The rule states that the power intensity per unit area from.
Hence, the intensity of radiation passing through any unit area directly facing the point source is inversely proportional to the square of the distance from the point source. Gauss's law is similarly applicable, and can be used with any physical quantity that acts in accordance with the inverse-square relationship.
Gravitation[ edit ] Gravitation is the attraction between objects that have mass.
The gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them. If the distribution of matter in each body is spherically symmetric, then the objects can be treated as point masses without approximation, as shown in the shell theorem. Otherwise, if we want to calculate the attraction between massive bodies, we need to add all the point-point attraction forces vectorially and the net attraction might not be exact inverse square.
However, if the separation between the massive bodies is much larger compared to their sizes, then to a good approximation, it is reasonable to treat the masses as a point mass located at the object's center of mass while calculating the gravitational force. All that this formula says is that brightness is the luminosity divided by the area which is illuminated.
Inverse square law (article) | Khan Academy
Because the area of a sphere increases as the square of its radius, it's the square of D which appears in the denominator. That's why this is called the inverse-square law; brightness is inversely proportional to the square of the distance.
With modern technology, brightness can be measured electronically. Unfortunately, it's not easy to explain how this technology works; we would have to discuss the nature of electricity, some mysteries of quantum mechanics, and the physics of electromagnetic fields. So we will fall back on an earlier technology which can be understood at an intuitive level without a lot of extra explanation.
A null-photometer is a device for comparing the brightness of two light sources. It can't provide a direct measurement of brightness, but it can tell you when two sources have the same brightness. In practical terms, the null-photometer we will use is just a sheet of aluminum foil sandwiched between two slabs of wax; a band of foil is wrapped around the edge, with a window allowing you to view the sandwich edge-on. The operation of a null-photometer is illustrated in the diagram below.
To begin with, you orient the photometer so each side is pointing directly at one ot the two light sources you want to compare; the light must strike the wax slabs squarely, and not at an angle. Thus one side is illuminated by one source, and the other side is illuminated by the other source. You then look through the window.Stage Left Audio - Physics 3 (Inverse Square Law)
If one source is brighter than the other, the corresponding side of the sandwich will be brighter than the other side. You eyes are pretty good at judging relative brightness; with a little care, you can determine a null reading quite accurately. A null-photometer in operation. The equation on the right is derived from the one on the left by rearranging the terms; this form is convenient for an experimental test of the inverse-square law.
The basic procedure for our laboratory test of the inverse-square law is shown in the diagram below. We will set up two lights of known luminosities.
The null-photometer is placed between the lights, and moved to the point where both halves of the window are equally bright.
The distances from the photometer to the lights are then measured. Finally, the luminosities and distances are substituted into the equation just derived; if the law is correct, the two sides should be equal, or nearly equal if we allow for experimental error.
The null-photometer is placed between the two lights and moved until both halves of the window have the same brightness. Testing the law To test the law properly, we will set up several pairs of lights, with each pair separated from the others to avoid confusion. If the source is omnidirectional then the intensity may be the same where ever we look - but most sources direct more intensity in some directions that others, and are called directional sources.
Here's another slow-motion video - a source of imulsive sound energy.
If we were standing next to the light-bulb as it smashed, we'd expect it to be pretty loud You can download the video from YouTube The inverse-square law The inverse-square law is hugely important in physics. Without it, even gravity does not make sense.
It can be pretty easy to understand using waves examples - but first let's have a go using a silly, but useful, example of a party balloon. Imagine taking a red balloon and blowing it up. What would you notice about the colour? The larger the balloon gets the paler the colour - eventually it turns pink or pops, but that's not the point of our example You can think of the surface of the balloon as being like the wave front radiating out from a wave source - say a loudspeaker.