Lighten up, It’s time for the inverse-square
Law of Brightness!
By Ryan Quinn
The light inverse square law is an interesting topic for
myself because I am a math major in my second year at Colby. The inverse square
law relationship is applicable to other things in astronomy as well as light.
This relationship relates to gravity, electric fields, radiation, and sound.
However, for this blog post we will focus on learning about the inverse square
law of brightness.
How much brighter is the sun
viewed from Mercury as compared to Earth? How much fainter is it viewed from
Mars? Questions like these can be answered by a mathematical relationship known
as the inverse-square law. This inverse square law helps us to relate a stars
brightness to its luminosity.
It may seem complicated at
first, so let’s start with a simple example.
Let’s start by looking at the energy of a lightbulb. If you
hold a lightbulb a foot away from you, it will be so bright you have to squint.
However, if the lightbulb is half a mile away from you, the light may not even
be visible. This relationship is known as the inverse square law of brightness,
and explains the phenomenon of how bright something can appear when distance is
a factor.
Lightbulbs can have a measurement of 60 watts, 100 watts, or
any number of watts. A watt is a unit of energy that is equal to one joule per
second. Imagine a lightbulb that emits 3.8x10^26 watts. This situation is sort
of impossible, because such a light source would be absolutely massive. This
“lightbulb” is actually our Sun. Our suns luminosity is defined as the total
energy a star radiates in one second. This is equal to one solar luminosity.
This means that a star that has 3 solar luminosities emits 3 times more energy
per second than our sun.
The closer a luminous object is to you, the brighter it
appears to be. The inverse-square law relates apparent brightness and
luminosity. Apparent brightness of a star is able to be measured by using a
photometer, a device that measures the amount of light hitting it. Imagine that
a star is in the center of a sphere with a radius of d (distance in meters).
The amount of energy that moves every second through one square meter of the
spheres surface area is the luminosity of the star, L, measured in watts. The
luminosity is divided by the entire surface area of the sphere, which is 4πD^2.
This calculation gives us B, the apparent brightness, measured in watts over
meters squared. The apparent brightness of a star becomes smaller and smaller
with increasing distances away from the star because the light emitted by the
star has to spread over larger and larger areas of space. This law is seen in
the diagram above, where the energy at each distance is divided into more boxes
as distance increases. This relationship can also be seen on a graph in the
figure below.
If you are interested in learning more about this topic, it
can be helpful to have a physical example of this physical law. A quick and
easy lab with additional information can be found at this website: https://www.nasa.gov/pdf/583137main_Inverse_Square_Law_of_Light.pdf
Thanks for reading!
References:
No comments:
Post a Comment