Superior Mirages, A Short Explanation Of Sunrise.

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Circonflexus

Superior Mirages, A Short Explanation Of Sunrise.
« on: April 10, 2007, 04:39:35 AM »
Please note: I'm not a native English speaker, but I'll try and write something intelligible. Also I don't know about Imperial units. That's fine: non-standard units just suck. Be serious and use metric.

What is a mirage ?

Short answer: http://en.wikipedia.org/wiki/Mirage/
Please note the depiction of the inferior mirage on the right: light rays are bent upwards (with the concavity on the upper side) due to a downward temperature gradient (that is, temperature is highest at floor level). This occurs on a span (optical length) of some few hundred meters.

Pressure and refractive index

Now the main cause of those mirages is not the temperature, but the refractive index: http://en.wikipedia.org/wiki/Refractive_index. This index directly measures the speed of light in the air. The hotter the air, the sparser air molecules are, and the nearer it is to void; in shorthand,
    the refractive index decreases with temperature.

But not only temperature matters! Actually with pressure it's the same, only simpler: the more pressure, the more air, so that
    the refractive index increases with pressure.

Superior mirages

Now in the atmosphere (in either round or flat earth) the pressure only depends of the weight of the air column over any point. This means that the pressure (obviously) decreases when one goes up; so that by the following,
    the refractive index decreases when going up.
This is the opposite situation from the inferior mirage we just saw on Wikipedia. Of course, this is called a superior mirage; this means  that the light rays will bend downwards.

Why does this explain sunrise?

Now imagine the Sun at a given height in the atmosphere; also note that here the optical length is much longer than in the common mirage, (think of about one thousand kilometers). The light rays that could reach the furthest point at floor level are those starting horizontally (they may actually reach infinity); but as the atmosphere causes a superior mirage, those horizontal rays bend downwards along the way and only reach a finite distance from the Sun.

The exact distance reached naturally depends on the precise value of the refractive index, and will be shorter when the index is high. This means that if there is more atmosphere at the (North and only) Pole, the rays here will reach floor level at a shorter distance. I don't have time to do the exact math for this now but will do it someday, but I have absolutely no doubt that it is possible to exhibit a refractive index repartition that explains exactly that sunlight lights a half-plane (whose border will pass through the Pole only on equinox days) at floor level. (I will also explain in a later messages why the flat Earth model with equidistant concentric parallel lines is inconsistent: parallel lines are actually closer to each other near the Pole).

This also explains why the hull of the boat disappears before its sails. There is actually a picture of this very situation in the Wikipedia article http://fr.wikipedia.org/wiki/Mirage; just imagine a flat Earth instead of this horrendous ballish shape.

*

Ulrichomega

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Re: Superior Mirages, A Short Explanation Of Sunrise.
« Reply #1 on: April 12, 2007, 07:33:18 AM »
I've always wanted to do this...

Wikipedia is not a valid source. You cannot justify these facts unless you prove them at atleast a couple different credible sites.

Until next time,  8)
I'm so tempted to put a scratch and sniff at the bottom of a pool and see what you do...

Avert your eyes, this is too awesome for them...