Twinkling Stars are a Mirage

You may already know that stars twinkle because of turbulence in the atmosphere, but do you know why turbulence changes the path of the light? Also why does a little wobbliness make the light appear to flicker on and off, and sometimes even change colors? In the video I re-create a demonstration I saw – on a school field trip to Fiske Planetarium when I was 7 years old – that explores these phenomena.


As you can see in the video there two demonstrations. One involving oil and water and the other about the role of the pupil. I will talk about the steps and results for each in succession, starting with oil and water since these build on each other.

Oil and Water Mirage:

Materials:
For this part you’ll need: a clear glass, water, oil (the clearer the better canola oil is what I used), a handheld laser, something to stir with and a wall or screen.

Experimental steps:

  1. Fill the glass about halfway with water. Then pour the oil on top, allow time for the layers to separate.
  2. First shoot the laser through the oil and then the water away from the boundary. There should be little difference between the two layers assuming no “bubbles” of water got up into the oil.
  3. Next aim the laser straight along the boundary between the oil and the water. Try and keep the laser level with the table while doing this. You should see the light spreading out and hitting the wall in multiple places.
  4. Play around a little and see if you can find a position that recreates the feel of a mirage. The right look will be a bright spot in line with the laser pointer plus a second stretched image below the laser. …but really just mess around to get the feel of it.
  5. When you’re happy with the way the light passes along the boundary try stirring things up a bit and see how it affects the image.

Explanation:
If done right the light will separate into multiple paths when aimed at the boundary between the different fluids. The reason for this is that each photon tends to take the path which results in the least amount of time needed between points. This is Fermat’s principle which is a generalization of Snell’s Law of diffraction; both of these are a mathematical way to describe the way light bends when it goes from one material to another. It has been known for thousands of years that light does this, Ptolomey even wrote out a table of the different angles of light entering water. But it wasn’t until Fermat that a model for why this happened became understood.

The principle of least time can be summed up by an analogy. Consider you are in rush hour traffic and you are running very late. The traffic on the highway is slowed to a crawl, but you remember a side street that even though you will have to drive farther will get you home sooner. So you turn off and take a different route. Even though this route is longer and possibly curvier it makes more sense to get somewhere fast. It’s also possible that at least part of your path is still on the highway. This is what the light is doing as it passes through the different materials. In some materials the light is much slower while in a vacuum the light isn’t slowed at all. The coefficient of diffraction is just a measure on how much the light gets slowed down as compared to speed in a vacuum.

In the case of our oil water model, the light is slowed more by the oil (Canola oil is made mostly of Oleic acid and has an index of refraction of 1.463) than it is by the water (water has an index of refraction of 1.333) so the light will curve through the water, away from the oil, and spend a larger part of it’s path in the water. In this way is can create a similar illusion to the kind you see when a desert has a hot layer of air near the ground.

Artificial Star and Pupil:

Materials:
For this part you’ll need: a handheld laser, two cards (note cards are fine, I used extra photo paper for a printer which is why my card started to bend in the heat), something to poke holes (a push pin or needle), a few cups and some tape.

Experimental steps:

  1. First tape the laser to one of the cups. Make sure the laser is either taped on or has a toggle switch so it can be left on.
  2. Place the cup with the laser to one side of a cooking range (you can use a gas or electric range, or if you are in a classroom a hotplate or bunsen burner will also work, though the bunsen burner may be harder to align). It’s important you do this first since everything else gets aligned around it.
  3. Next tape a card upright (perpendicular to the laser light) on a separate cup. Put this second cup on the same side of the cooking range as the laser is on.
  4. Be sure the card is blocking the light from the laser. Carefully poke a small hole in this card to allow just a tiny light to pass through. This step is to narrow the light so it is more of a point source, like a star is. However, if the hole is too small you may not get enough light across the cooking range or you may create strong diffraction patterns which can interfere with the results.
  5. Make another cup with an upright card to block the laser light on the opposite side of the cooking range. You may need to put this on a taller or shorter cup depending on weather the laser is taped at a slight angle or not, though this will not affect the results.
  6. Align this new cup so that the laser is again being blocked by the card. Again poke a small hole in the card where the laser lands. This hole will be the “pupil”.
  7. Next make sure there is a wall or screen near enough for the laser to land on so that any changes can be observed. At this point  the laser should be steady, if a little smaller than usual.
  8. Turn on your cooking range (or other heat source). The greater the heat difference the better as convection will churn up the air and the varying densities will bend the light around since hot (less dense) air has a smaller index of refraction than cold (more dense) air.
  9. Almost immediately the laser light on the wall should start twinkling. If it dosen’t it may mean that one or both of the holes are too large, or that the heat source needs to be larger.
  10. Alignment is a constant battle since many things can get bumped or as in my case change shape from the heat. While aligned look at how the light wobbles around on the “pupil” card.
  11. Finally try taking away the first focusing card near the laser and see how the light changes. Usually it stops twinkling but still wobbles and shimmers.

Explanation:
As with a lot of optics (rainbows, focus of a lense, color perception) understanding why stars twinkle is dependent not only on the physics of light but also on the point of view. In this case both the fact that we live in a sea of  air with varying density and indices of refraction combined with the narrowness of our pupils and the light source conspire to create the illusion of twinkling. At low altitudes with a lot of moisture in the air the wobbling can be rather dramatic. Along with turning on and off, if the light just grazes the edge of your pupil the mostly white light of the star can get diffracted off the edge of your iris and cast a rainbow across the back of your retina. Through a telescope the star may not twinkle as such, since the aperture of the telescope is much larger than your eye, but the star will still wobble and shift around. The quality of this shifting image is called the “seeing”. So to get the best seeing modern telescopes are built at high altitude deserts (like the Attacama desert in Chile) to minimize the mirage of twinkling stars.

Linkography

Linked videos in the intro:
https://www.youtube.com/watch?v=H4x39AJ9Wzk
https://www.youtube.com/watch?v=N3IgVidGjQk
https://www.youtube.com/watch?v=L-Wtlev6suc
https://www.youtube.com/watch?v=hhn-RzMELhY 

Link to Fiske Planetarium, where I saw this demonstration when I was 7.
https://fiske.colorado.edu/beta/ 

Other videos about mirages:
https://www.youtube.com/watch?v=HzIBmuLHMSE
https://www.youtube.com/watch?v=6x52290in9w 

Other references:
www.feynmanlectures.caltech.edu/I_26.html
http://www.physicsclassroom.com/class/refrn/Lesson-1/The-Direction-of-Bending
https://en.wikipedia.org/wiki/Snell’s_law
https://en.wikipedia.org/wiki/Fermat’s_principle https://en.wikipedia.org/wiki/List_of_refractive_indices http://pubchem.ncbi.nlm.nih.gov/compound/oleic_acid#section=Kovats-Retention-Index https://www.youtube.com/watch?v=eAQZp6yTR2Q 

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