**WHY IS REFRACTION IMPORTANT:**FET fundamentally relies upon refraction through the air. Without it, there cannot be sunsets, sunrises, moonsets, moonrises on the Flat Earth.

When you look at a sunset, you can see that the sun touches the horizon, then becomes a semi-circle, then a thin sliver, then it's gone. In Round Earth, this is an obvious consequence of the curvature of the planet - but in FET, (without refraction) the sun could get closer and closer to the horizon - but never quite touch it. It would also get smaller and smaller (because it would be further and further away from you).

So for flat Earth to work, light cannot be travelling in straight lines...definitely NOT.

**REFRACTION:**Now, refraction is a true and real thing - but it ONLY bends light at the junction of two materials (which is an abrupt change) - or due to varying density of the material...which is kinda reasonable - right?

The air is thinner at high altitudes than it is at sea level.

So Tom (in particular) believes that this effect is bending the light from the sun (and moon - and stars and planets - which also rise and set) so that light from the sun drops downwards towards the surface and then flattens out as it gets closer to us. When we look along the almost horizontal beam - it makes it look like the sun is on (or even below) the horizon.

Tom claims:

* That he has some incredibly complicated math for this (which he never shows ANYONE despite multiple requests).

* That there is a simplified version of it (which is on the Wiki)...which he modestly calls "The Bishop Equation".

* But which incorporates a constant value ("The Bishop Constant") - but which he has no idea of the value of.

As usual with FET - we have a vague, messy theory with plenty of scope for prevarication in the event of challenges. (Oh, sorry we don't know the value of the Bishop Constant - and you're not seeing the "full" math.) This is a pattern for Mr Bishop - like how he claims to have no idea what a map of the world looks like. He fondly imagines that more vagueness makes his nonsense harder to disprove...it really doesn't.

Refraction is a great thing to wave around because most people know it happens - don't understand it very well - so when someone says "It's refraction" and throws some nonsense equation at us - we mostly kinda zone out and assume he must be right.

So we're left with a bold claim - and no way to prove it...or so Mr Bishop fondly imagines. Fortunately, some of us here are smarter than he gives us credit for! :-)

These are the problems with his theory:

**PHYSICS:**Refraction has been studied since at least Sir Isaac Newton's time. The effects of refraction on the paths of light rays is very well known - the Victorians worked out all of the effects, measured all of the materials - did mountains of experiments.

Snell's law is all you really need - the sine of the angle that the beam strikes the surface divided by sine of the resulting beam equals the refractive index of the second medium divided by the refractive index of the first. Easy.

Since we figured out quantum theory, we also know why and how it happens. It's actually a consequence of conservation of energy and the constant speed of light in a vacuum. You can derive the experimental "Snells law" from first principles - and the math precisely fits reality.

The "Bishop Equation/Constant" is nowhere in this math. Honestly: Mr Bishop made it up. Because he doesn't know the value of the "Bishop Constant" we know he didn't get the number experimentally - and we know he didn't derive it from math because it doesn't match Snell's Law.

**REFRACTIVE INDICES:**The refractive index of air at sea level is 1.00029 - this number is in physics textbooks - it's everywhere. The refractive index of a vacuum is (by definition) 1. So the amount of variation in refractive index between air and space is TINY...3 parts per 10,000.

But there is a much bigger problem for Tom's pet theory:

Here is a diagram showing what happens when a light ray goes from a low refractive index to a higher refractive index. In this diagram is from air (1.00029) to water (1.333) - but we can imagine it being from vacuum (1.00000) to air (1.00029) - the bend angle would be less - but the bend direction is the same. This is "Snell's Law" (Hint: Check Wikipedia!)

(Grab a laser pointer and a bucket of water...you can do this experiment yourself).

You'll notice that the light ray bends DOWNWARDS - this is important. Now, mentally, put the sun (in low refractive index vacuum) at the top left of the picture - and imagine you're a flat-earth occupant standing at the end of the light ray at the bottom of the diagram in all of that higher refractive index air. The light ray that you see would show the sun as being HIGHER in the sky than it really is...get that? HIGHER. Not LOWER - which is what Tom claims. If refraction was significant then the sun would get HIGHER in the sky as it gets further away. Not only would there be no sunsets - but the sun wouldn't get as close to the horizon as you'd otherwise expect.

In reality, the bend angle of light is far FAR too small to be noticeable. You can use Snell's law to calculate it...go ahead, knock yourself out.

Snell's law says that the total amount of bend in transition from one material to another (even if it's a gradual change, as from vacuum to sea level) is dependent on the ratio's of the two refractive indices - so the ratio of the sine of the incoming light ray angle to the sine of the outgoing light ray angle is 1.00029/1.0 - if the sun's rays were striking the atmosphere at 45 degrees to the vertical - then the angle it's going to travel through the densest part of the atmosphere will be arcsine ( sine ( 45 degrees) / 1.00029 )...which is 44.9734 degrees to the vertical.

The bend due to the atmosphere is a wildly impressive 0.03 degrees! The angle subtended by the sun is 0.53 degrees - so the bend due to the atmosphere is about 6% of the diameter of the sun. Nowhere close to enough to account for flat Earth sunsets.

If the sun is overhead at noon in US central time - and at around sunset in an equatorial GMT timezone (say at the city of Accra which is close to the equator and the Greenwich meridian)...then FET says us that the sun is 3000 miles up and 6000 miles away to the west of Accra. The "true" angle of the sun in the sky is 31.3 degrees above the atmosphere - and Snell's Law says that it'll be refracted UPWARDS by an even less impressive impressive 0.01 degrees...and not DOWNWARDS by at least 31.9 degrees as required to make it appear to be below the horizon.

Oh dear...seems that the world must be round after all.

Tom might want to claim that there is some other kind of magic air up there that bends light the other way - this would require a NEGATIVE refractive index. Trouble is that refractive index depends on the speed of light in the material...since nothing (including light) can travel faster than the speed of light in a vacuum, there cannot be negative refractive indices.

**LIGHT FREQUENCY:**One of the VITAL aspects of refraction is that it changes depending on the frequency of light. Refract white light through a prism - and you get a spread of colors. If light from the sun were bent through the angles that Tom claims - then there would be a very pretty backwards-rainbow around the edges of the setting sun! Do you see this? No? Then there is no significant refraction - so the Earth is ROUND.