Standard Candles

Age

Elementary School, Middle School

Format

Stage Show, Hands-on

Materials

   Two identical flashlights with multiple brightness settings. Remove the reflective mirroring behind the bulb so the light beam is not collimated.
   Several sheets of red plastic wrap 

Safety Precautions

Science Theatre demonstrators must keep the safety of themselves and their audience in mind at all times. All Science Theatre demonstrators must have read through the Safety Training page. The ST Safety Box with first aid kit, fire extinguisher, etc. should always be available to demonstrators. Always wear safety gloves, glasses, and a labcoat if handling chemicals; always perform potentially dangerous demonstrations at a safe distance from the audience; and always keep a very close eye on any volunteers you call from the audience. Whenever volunteers from the audience are given items such as the flashlights and plastic, watch them carefully to make sure they do not misuse them.

Preparation

If your stage area is very large, then you can perform this demonstration by having the volunteers with flashlights stand at various distances from the audience. If you have limited space to work with, you may need to have the two volunteers with flashlights stand at various distances from a third volunteer who acts as the observer for the entire class.

Demonstration

1. At first, ask for two volunteers from the audience. Give each of them a flashlight and turn out the lights. Make sure each flashlight is set to the same, low-power brightness setting. First, have the volunteers stand at the same distance from the observer (the entire audience, if you have enough room, or just a third observer). Discuss observations.

2. Next have one of the volunteers move further away from the observer. Discuss observations.

3. Now have the far volunteer turn up the brightness on his flashlight so that it is much brighter than the near volunteer's. Discuss observations.

4. For the next demonstration, you can ask two new volunteers to hold the flashlights and a third to hold the red plastic wrap. This time have the two flashlight-holders stand at the same distance and turn out the lights. Make sure each flashlight is set to the same brightness setting and demonstrate this to the observer. Have the volunteer cover one of the flashlights with several layers of red plastic wrap - enough so that the difference in brightness vs the unobstructed flashlight is obvious. Discuss observations.

5. Now turn off the unobstructed flashlight. Remove some of the cellophane layers, or add more, to the obstructed flashlight. Discuss observations.

What to Say

When you look at something, how can you tell how far away it is? If you're really close to the object, your two eyes can use parallax for depth perception (see parallax demo). If you're farther away, we need a different technique. When you see two stars in the sky, do you have any idea which one is farther away?

Astronomers use special objects in the sky called standard candles to measure distance. Just by observing these objects, we can tell how far away they are. How does this work?

This demonstration has lots of opportunities for the audience to make observations and participate as volunteers. Make sure to call on audience members that raise their hands politely.

Part 1 of the demonstration: Here we prove that the two flashlights have the same brightness. The observer should agree that each flashlight looks the same.

Part 2: The farther away the object is, the dimmer it looks! The observer should agree that the near flashlight looks much brighter. This is because the light spreads out from the flashlight; as it gets further and further away, it gets spread out over a larger and larger area, so it appears dimmer and dimmer. So, we can tell how far away an object is if we know how bright it really is and we know how dim it looks to us on Earth.

Part 3: But how can we be sure that an object is really as bright as we think it is? The observer should note that the flashlight in the back can be turned on so bright that it appears even brighter than the close object. If we thought these objects were the same brightness, we would misjudge which one is farther away. Astronomers need to be very careful to make sure that any two objects are really at the brightness we think they are - that they really are standard candles. There are all sorts of objects that have other special properties that we can use to tell how bright they really are.

Part 4: So, if we know how bright something really is and how bright it appears to us on Earth, can we definitely determine its distance? Not always! There's another problem to consider. The observer should note that the flashlight covered in plastic wrap appears dimmer, even though its at the same distance. If there is material in between us and the light source, it can appear dimmer than it would simply due to its distance. Is there anything out in space to obscure our vision of stars? Yes! The Interstellar Medium (ISM) is a bunch of gas and dust that fills the space in our galaxy. In some places, the ISM is very thick and the stars behind it appear very dim. In other places, the ISM is thinner and doesn't obscure the stars as much. Notice also that the ISM, modeled by out plastic wrap, makes the light source appear more red. This is a property that always seems to be true of the ISM - it absorbs lots of blue light, but lets most of the led light go through. Astronomers call the effect of the ISM "extinction."

Part 5: So how can we overcome this problem? When you add or remove layers of plastic wrap, note that the extinction either increases or decreases, respectively. This means that the light source appears more or less bright and more or less red. When we look into space, we don't know if the light source is dim because it is far away or because it is highly extincted. However, we can tell how high the extinction is by how red the object is! If the object is really red, we know we're looking at it through lots of ISM. We can measure this reddening and use it to figure out how much dimming is caused by the ISM. Then we know how bright the object would appear to us on Earth if it were unobstructed, so we can tell how far away it is just like we did earlier in the demonstration.

Why It Is

Light from point sources, such as stars, spreads out into space spherically, in all directions, following an inverse square law (see diagram). The surface area of a sphere is 4*pi*r^2. As light travels away from the source, it fills a larger and larger surface in space that is proportional to the distance from the source squared. As the light gets spread our over this larger area, it appears to decrease in brightness proportionally.

Many astronomical objects serve as standard candles. We will mention just a few here. Perhaps the most famous are Cepheid variable stars, whose brightness oscillates with time at a rate which is related to the average brightness. Main sequence stars (meaning stars in the same stage of life as our sun) have a color which is related to their average brightness because they are essentially blackbody radiators. At very large distances, astronomers may take the brightest galaxies in a cluster of galaxies to be at a certain typical brightness.

Interstellar extinction is caused by dust and gas in the ISM. This is the same dust and gas that stars are eventually born from. Much of the ISM was actually contributed by stars that have died and expelled their contents into the galaxy. The ISM is mostly made of hydrogen gas, but it is the small percentage of dust (microscopic particles made from carbon, silicon, and other components) that does most of the absorbing of light.

Why does the dust redden light? This has to do with the size of the dust particles. When the dust grains are about the same size as the wavelength of the light or smaller, then the dust absorbs the light very well (see e.g. the Mie Theory of interstellar extinction). Think of this like waves in the ocean. These waves have wavelengths of many meters - much larger than a grain of sand. Therefore sand does not block ocean waves. However, waves hitting a big island will simply stop. The only way for waves much smaller in wavelength than the island to pass through is to avoid the island altogether! Similarly, long-wavelength light like red or infrared light can pass through the ISM without too much trouble. Short wavelength light like blue light has trouble passing through. Extremely short wavelength light like X-Rays might pass through very well, if they simply do not hit any of the dust.

Real Life Examples

We use the inverse square law to judge distance every day! If you're driving on a highway, you can tell how far away cars are based on how bright their headlights look.

If you live in a dark place, you can actually see the ISM with your own eyes! In really dark places like Michigan's Thumb or the Upper Peninsula, you can see the bright band of the disk of the Milky Way Galaxy cutting across the sky at night (see diagram). Right in the center of the Milk Way are dark patches - "dust lanes" - where the ISM is very thick and extinction is very high. There are lots of stars in this region, but they are heavily obscured by the intervening dust and gas.