# Relationship between intensity and distance

### Inverse Square Law Formula

The relationship between the intensity of light at different distances from the same light source can be found by dividing one from the other. The formula for this is. The intensity of a star's light falls off with distance according to a simple the relationship between luminosity, brightness, and distance. The inverse-square law, in physics, is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance . physical quantity that acts in accordance with the inverse-square relationship.

Once both distances have been recorded, flip the photometer over so the left face is now the right face, and vice versa. Re-position the photometer between the lights, move it so both halves appear the same, and again measure the distances.

## Light Intensity and Distance

Repeat two more times, again flipping the photometer each time. You should now have four separate measurements of the two distances. Each set of four measurements can be averaged to get a more precise value; you can also look at the range of values for each measurement to get some idea of the accuracy of your work. Before moving on to the next pair of lights, be sure to record the luminosities La and Lb.

When you write up your lab report, first compute averages for your measurements of Da and Db for each pair of lights. If the last two columns of each row are equal, allowing for experimental error, then the inverse-square law passes the test.

Measuring luminosity The same procedure can be used to measure the luminosity of a light-bulb. We will set up a pair of lights and tell you the luminosity of one light; your job is to calculate the luminosity of the other.

Follow the same procedure you used when testing the law: Record your measurements for Da and Db, along with the known luminosity La. When you write up your lab report, compute averages for your measurements of Da and Db just as you did when testing the law.

Then plug your averages and the known luminosity La into the equation In astronomy, we sometimes know the distance to a star but not its luminosity. A measurement like this can be used to find the star's luminosity.

Measuring distance A similar procedure can be used to measure an unknown distance, given the luminosities of both light-bulbs. We will set up one last pair of lights and tell you both luminosities. Once again, repeat another three times, flipping the photometer each time. Record your measurements for Da, along with the given luminosities La and Lb. When you write up your lab report, compute averages for your measurements of Da, and plug your result into the equation In astronomy, stars come in a range of luminosities, and we can sometimes figure out the luminosity by measuring the star's color.

If we know the luminosity, we can then use this technique to measure the star's distance. This report should include, in order, the general idea of the experiments, the equipment you used for this work, a summary of your experimental results, and the conclusions you have reached.

In somewhat more detail, here are several things you should be sure to do in your lab report: In your own terms, explain the difference between luminosity and brightness, and summarize the inverse-square law. List individual values for each Da and Db you have measured.

Estimate your experimental errors from the range of values you got for each distance, and check for bad data values. It's likely that the In this case, you should exclude the The three remaining values give you an average of Make a table with your results as described in the subsection on Testing the law.

### Wave Propagation | AS A Level Physics Revision | University of Salford

Do your results support the inverse-square law? Give reasons for your conclusion. Why should you flip the null-photometer over between measurements? How might that help improve your accuracy? Consider a laser which fires a beam of parallel light rays.

### Light Intensity and Distance From the Source | Waves | Uzinggo

If the diameter of the beam is constant regardless of the distance from the laser, does the inverse-square law apply? 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.

The depth of colour of the balloon is like the intensity of the wave. We've also heard this explained by thinking about the thickness of jam you could spread on a table -tennis ball, a cricket ball and a football, if you only have the same amount of jam wave power available in each case - but this sounds messier than the balloon idea! The key thing to remember is that the energy from the source is always the same - it is simply distributed over a larger area, the further away from the source you try to measure.

So - what has all this to do with the 'inverse-square' law? It comes down to the geometry of the area over which the power spreads out. Let's make it easy for ourselves, and assume the power spreads out equally in all directions, in which case the area is the surface of a sphere and our balloon should be spherical!

Remember - the inverse-square law applies, where energy spreads out spherically. Amplitude and intensity The energy of a wave is proportional to the square of its amplitude. Therefore the intensity of a wave is also proportional to the square of its amplitude. If we move twice as far from a loudspeaker, the sound intensity will decrease to one-quarter its original value, and the sound pressure ampitude will go down to one-half.

Here are some slow-motion videos which may be useful in showing waves propagating from a source. Look at these ripples spreading out in water. How are they different, and does the inverse-square law apply?