Physics Photo of the Week Reflections and Mirages

Physics Photo of the Week 

September 13, 2024

Reflections and Mirages

Lakes are always very photogenic when the mountains and other objects are reflected in the water.  However, there are two kinds of reflections in this week's photo, although only one kind of reflection (the direct simple reflection) is seen.  We first notice the reflection of the diving platform close by and the prominent reflection of the background mountain, Mt. Hor, that overlooks Willoughby Lake in Vermont.

 

The images below show a close-up of the raft and a close-up of the more distant shore of the lake from the left center part of the photo:

 

The reflections from the close-up of the raft are clear, however the raft's reflections are distorted by the small ripples of the water surface.  The reflections of the background trees, especially the tree-tops are also distorted by the water ripples.  Somewhat like fun-house mirrors that have curved surfaces.

The close-up of the distant shore, especially close to the shore, shows a totally different kind of "reflection".  This sharply appearing reflection has none of the distortions caused by the ripples in the water, but appears very sharp and well-defined as if the water surface was very calm in the distance.  However the water surface still has the ripples all over the lake.

This clear "reflection" is not a reflection by it is actually a refraction of the rays caused by a temperature gradient of the air in the few inches above the water.  This refraction of the light caused by temperature gradient is called a mirage.  This image was made on a cool day.  The surface of Willoughby Lake had warmed up during the hot days of July to about 72 deg F.  The preceding night was cool.  The air temperature was in the mid to low 60's.  Air cools rapidly, whereas the water in the lake - due to the large specific heat of water and the large mass of the water in the lake - takes a very long time to cool and the surface temperature of the Lake is still in the 70's - warmer than the bulk of the surrounding air.  Because the lake surface is warmer than the surrounding air, the air the surface of the lake (within a few inches), is a little bit warmer than the air further away from the surface.  This produces a temperature gradient within the air above the lake surface.

The speed of light in air is about 99.90 percent the speed of light in vacuum.  The speed of light in air also depends slightly on the air's temperature.  Due to the temperature gradient (warmer air near the lake's surface) the speed of light is slightly larger the closer to the surface of the water (99.91 percent the speed of light in vacuum).  This small change in temperature actually causes the light ray to be bent, or refracted upwards by a small amount.  When an observer on the shore sees the refracted light from beneath the opposite shoreline, it appears as a sharp clear "reflection.  The diagram below shows the light path through the mirage.

The diagram above shows a greatly exaggerated view showing the warm air above the lake and the warmer air immediately above the lake surface.  The thickness of the warm air layers is greatly exaggerated - the warm and warmer air thicknesses are only a few inches thick.  The distance from the observer to the far shore is greatly shrunken from the approximately 1 mile distant.  The actual angles in the air for the light ray bending are much smaller than shown in the drawing. The angles the light ray is bent is a tiny fraction of a degree.  The angles are small due to the very small change in the speed of light between the warm and cool air.

Mirages are often seen in highways on a warm day.  The hot air next to the pavement acts the same way as the warmer air above the lake surface.  The mirage on the highway actually refracts the light from the distant sky, or background of trees or mountains.  The "reflected" or refracted image of the sky gives the appearance of water on the road.

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Physics Photo of the Week is published periodically during the academic year on Fridays by Donald F. Collins, professor emeritus of Warren Wilson College. These photos feature interesting phenomena in the world around us.  Students, faculty, and others are invited to submit digital (or film) photographs for publication and explanation. Atmospheric phenomena are especially welcome. Please send any photos to dcollins@warren-wilson.edu.

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