Desert Mirage

Classical Mechanics Level 1

A mirage is a frequent optical occurrence for desert travelers, which appears as a distant body of water. Which of the following best explains this phenomenon?

Note: The mirage featured in this picture is known as an inferior mirage.

Light bends because there are layers of air with different temperatures These are real but shallow bodies of water that evaporate by the time you reach them Wind kicks sand up into the air, which scatters light, creating the illusion of water Mirages are reflections of light from the sky off the sand

5 solutions

Ian Lang
Nov 9, 2017

The air just above the sand is hotter and therefore less dense than the cooler air higher up. Light from the sky moving from the denser to less dense air is bent upwards into your eye so the sky appears to be on the sand.

Moderator note:

At a more fundamental level, the reason this happens is quantum mechanical: when traveling between two points, photons will always take the path that takes the least amount of time. This means the photons will not travel in a straight line to reach your eye. Since photons travel through hot air faster than through cold air (due to hot air's lower density, as mentioned in this solution) they travel in a bent path. The light comes from the sky, with the path bending up, so that it looks like it’s coming to the ground.

If you're still not understanding why the bending would happen, here's an analogy:

Imagine a dog on grass who wants to catch a tennis ball that is on sand. Suppose the grass is easier to run on than the sand, so any travel on grass is faster.

If the dog made a beeline for the ball with a straight line, he wouldn't be travelling the fastest possible, because he could spend more time on the grass before entering the sand area.

Dogs do this particular adjustment in real life! ( Source. )

Bending of air depend on the refractive index. Why is it affected by the mass density of the air?

Pranshu Gaba - 3 years, 6 months ago

Mirages can occur even in vacuum if the angle is shallow enough. IIRC, as long as the smallest vertical perturbance is less than half the wavelength of the light, it will reflect perfectly. Every surface approaches 100% reflectance as the angle of incidence approaches zero.

Matthew Orlando - 3 years, 6 months ago

it is not to this topic, but these ''Brilliant pictures'' are seen quite often, where are they created ?

André Hucek - 3 years, 6 months ago

The software we use is called Figma.

Jason Dyer Staff - 3 years, 6 months ago

who writes masternote??

Saksham Jain - 3 years, 6 months ago

This is not quantum mechanical- it is classical optics...

A Former Brilliant Member - 3 years, 5 months ago

To understand the Principle of Least Time in a "why does this happen" sense and not just "it's a law that happens", quantum mechanics is needed. I recommend this Feynman lecture which mentions the narrow slit experiment.

Jason Dyer Staff - 3 years, 5 months ago

Frank Kelley
Nov 20, 2017

Light moves slower through materials that are more optically dense. This is the index of refraction. Cool air is more dense than hot air.
As cool air passes by hot air it causes distortions of light called mirages that you can look like waves in the air above streets, car hoods, cooking grills, the hot sand, etc.

In this example, light is passing from cooler air above to hot air down by the sand. This bends the light coming down from the sky like a prism back up to your eyes to make it appear like it is sky blue on the sand. Because the cool and warm are are constantly mixing it causes are shimmering effect like looking at water.

The mirage disappears as you approach because your viewing angle increases as you get closer. Far away, the angle from the ground to your eyes is very shallow so light doesn't have to bend much. As you approach, the angle increases until you are standing directly above the spot on the ground making a right angle. A mirage will never bend light that much! It's effect is weak at bending light. This is why a mirage is always towards the horizon.

Next time you see a mirage and it looks like it's dissappearing, try walking backards to see if it will reappear again. Bonus question, why is the sky blue? (Hint: lookup Rayleigh Scattering)

The sky of Earth appears blue because air molecules more easily scatter the shorter wavelengths of visible light, the blue end of the spectrum.

Howard Russell - 3 years, 6 months ago

How does optical density relate with mass density? Is it true that higher mass density means higher refractive index?

Pranshu Gaba - 3 years, 6 months ago

Xanthorrhoea West
Oct 24, 2017

The air near the surface of the horizon has been heated and thus its refractive index has been altered, meaning the sky becomes visible in patches that are below the horizon.

Why does heated air have a different refractive index than cooler air?

Pranshu Gaba - 3 years, 6 months ago

As the higher temperature density is more than the lower temperature density in upper and lower level.

Taha Ibn - 3 years, 6 months ago

I was tought that it is total reflection

Hans mustermann - 3 years, 6 months ago

Bill Dager
Nov 23, 2017

This is not a solution. This is a reward for cinematography. Eddie Young, under David Leans direction in the famous film Lawrence of Arabia, used this miracle of physics to introduce Omar Shariff. Oscar awarded for this fine shoot. Please see this classic film and you'll understand the visual miracle.

Cam S
Nov 20, 2017

Water evaporates quickly when things are warm. That's why it's not that there isn't any water in the desert; it's just that you can never get to it in time.

This is not true. Mirages are illusions, there is never any water present. Our mind perceives it to be water because we can see the sky at ground level, and we feel that we are seeing the reflection of sky in a body of water. Oases do exist in deserts.

Pranshu Gaba - 3 years, 6 months ago

At a more fundamental level, the reason this happens is quantum mechanical: when traveling between two points, photons will always take the path that takes the least amount of time. This means the photons will not travel in a straight line to reach your eye. Since photons travel through hot air faster than through cold air (due to hot air's lower density, as mentioned in this solution) they travel in a bent path. The light comes from the sky, with the path bending up, so that it looks like it’s coming to the ground.

Aiden Cooper - 3 years, 5 months ago

Desert Mirage

5 solutions

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