Hot Road Mirage

mirages - refraction - gradient index of refraction

What it shows:
There are various types of mirages possible, the details depending on whether the hot air is above or below the cool air and how sharp the transition is from cool to warm. This demonstration simulates what happens when a dark asphalt road gets much hotter than the air around it -- the air next to it becomes hotter than the higher air and light traveling through this temperature gradient is bent so much that it appears reflected. The shimmering water on a road's surface or the blue oasis in the desert are natural examples of blue skylight being reflected -- here we see that effect.

How it works:
A six foot long (1.83 meters) roadbed is made of rectangular (3"x2") aluminum tubing. Inside the tubing, two 500 watt electric heating cords 1   run the full length and get the "roadbed" quite hot. A photographic light box (for viewing transparencies) at one end of the roadbed serves as the skylight and a video camera at the opposite end is the observer. The experimental layout is illustrated below.



A small arrow (about 16 mm long), cut out of plastic tape, is taped vertically on the light box so that its bottom is about 6 mm above the road surface. When the arrow is viewed by the camera, one sees the arrow directly (above the road) as well as an upside-down image of the arrow beneath the surface of the road -- the upside-down arrow is the mirage. The formation of the image is illustrated below.



The index of refraction of air is about 1.0003 and changes to 1.0002 when the temperature is increased by 100°C. Thus the velocity of light is 0.01% greater in the hotter air and a large temperature gradient over a short distance will deflect a wavefront towards the cooler air. 2   Thus the observer sees the arrow both directly by means of rays a and b through the cooler air (with negligible temperature gradient), and indirectly by means of the bent rays c and d. Because the observer assumes light entering the eye is coming in a straight line, (s)he imagines the origin of the deflected rays to be below the road. If the bottom of the real arrow were even (same height) with the road, light rays originating from the bottom of the arrow would be deflected out of the observer's view and that part of the arrow would be invisible to the observer.

An alternative demonstration uses a HeNe laser and shows the effect of a light ray deflected upward by hot air over an electric "burner" hotplate. The laser is mounted on the lecture bench and the beam is directed onto the side wall of the lecture hall. The (preheated) hotplate is then slid under the beam close to the laser. The spot of light on the wall is seen to move up when the hotplate is slid into place and the deflected beam dances around due to the continuously varying index of refraction of the hot air movement. This demonstration is more often used to illustrate the twinkling of stars -- the atmosphere, being in constant motion, continuously moves hot and cold air across our line of sight resulting in the apparent random motion of the stars, which we describe as "twinkling." The long path through the atmosphere produces this effect in nature; here, the very hot air and the optical lever magnifies this effect and makes it visible on this relatively small scale. The demonstration is more fully described in the following writeup (Hotplate Mirage II).

Setting it up:
The "roadbed" sits on two chemistry ringstands and will fit on one of our longer carts. The light box can be on a separate cart, 40 to 50 cm from the end of the roadbed. The camera sits on a tripod on the floor -- use a zoom lens for a closeup view of the arrow. It takes at least one-half hour for the roadbed to get good and hot. Three heating cords can be used to speed up the process, but be aware that that's a total of 1500 watts and will blow the circuit breaker if the circuit is already laden with other loads.

For the twinkling star setup, adjust the laser height on the lecture bench so that the beam just grazes over the top of the hotplate. The laser and hotplate should be far from the wall to maximize the optical lever.

Comments:
The upside-down arrow is a inferior mirage, a term used to describe the effect when the image is perceived at a position beneath the true position of the object. The excellent references below also describe the formation of superior mirages as well as a combinations of other possibilities. Rating ***

References:
S.J. Williamson and H.Z. Cummins, Light and Color in Nature and Art, (John Wiley & Sons, NY, 1983) pp 417-425.
D. Falk, D. Brill, and D. Stork, Seeing the Light - Optics in Nature, Photography, Color, Vision, and Holography, (Harper & Row, NY, 1986) pp 58-62.

1 GLAS-COL (cat. no. SC-C6) heating cord. The upper temperature limit is 600°C (1100°F).
2 This bending of light rays is very clearly demonstrated in Bouncing Light Beam except that the denser medium (higher index of refraction) is below the less dense and the light ray is bent downward.