Can you see past the horizon? Depending on the weather, and the amount of refraction, yes, you can see past the horizon.,
The horizon is the point where Earth curves away too much for you to be able to see it anymore. Every body in the universe has a horizon, but it depends on the size of that body and your height above the ground. The formula to work out the distance to the horizon is d=√2RH/1000. R is the Earth’s radius (6,370 km) and H is the height above sea level. I am 1.8 m tall. That means d=√2*6,370*1.8/1000, which is 4.78 km. That means, if I am standing at sea level, I can see the horizon 4.78 km away. If I were able to stand on the surface of Jupiter (I know it doesn’t have a solid surface, but bear with me), the horizon would be d=√2*69,911*1.8/1000, which means that the horizon would be 15.86 km away. The difference is caused because Jupiter is much larger than Earth and so the ground curves away much more gently.
The distance you can see to the horizon obviously extends as you get higher up. If you are at the top of the Burj Khalifa at 828 m, the horizon would be 103 km away. If you were on the top of Everest, the horizon would be 336 m away. And if you were on the International Space Station, the horizon would be over 1,600 km away.
So, can you see past the horizon? Yes, you can. If the weather is perfect, you can see over 200 km. How can that be? It is due to something called atmospheric refraction. Light travels at the speed of light in a vacuum. However, when light passes through different mediums it slows down by different amounts. The speed of light in a vacuum is 299,792 km/s. It is 299,702 km/s in air. It slows down to 225,000 km/s in water. It only travels at 125,000 km/s through diamond. The difference is because of the density of the medium the light is travelling through. A vacuum obviously has no atoms in it, while much denser water has a lot of atoms. When light enters water, the light photons scatter off the atoms, which makes their path longer, slowing them down.
When light passes from one medium into another and its speed changes, its direction changes as well. This is because when the light enters the water, the side of the light that enters the water first slows down before the opposite side, bending the light. The opposite is true as well. When light leaves water into air, the side of the light that enters the air first speeds up before the opposite side and bends the light beam. This is called refraction and is why a straw placed into a drink appears to be sheared in the middle, with the lower half not directly below the upper half. The amount that a material slows down light, and therefore its ability to refract light, is called its refractive index. A vacuum has a refractive index of 1 because it doesn’t slow light down at all. Air has a refractive index of 1.000293 and water has a refractive index of 1.333. Diamond has a refractive index of 2.417.
What does this have to do with the horizon? Air slows down the speed of light, but cold air slows it down more than warm air. Warm air has more energy and the air is less dense than cold air. There are more molecules in cold air to scatter light rays. That means that light will bend as it goes from warm air to cold air, and this is called atmospheric refraction. Generally, air gets colder as it gets higher, and then it gets thinner as the atmosphere thins. In normal conditions, light reflecting off objects beyond our horizon will be reflected back up into the air. It will pass through warm air, slowing down as the air gets colder, and its angle will not bring it to our eyes. However, sometimes, when the conditions are good, there is an inversion where cold air lies below warm air. In this case, the light is slowed down from its natural path, being bent so that it heads towards our eyes. In these conditions it is possible to see things that are beyond the horizon because their light is being bent to an angle that leads it to meet your eyes. On a clear day with no humidity, an inverted layer of very cold air, and no pollution, light from 200 km beyond the horizon can be bent to such an extent that you can see it.
So, it is possible to see things beyond the horizon, if the conditions are correct. And no, the Earth is not flat. And this is what I learned today.
Sources
https://emtoolbox.nist.gov/wavelength/documentation.asp
https://en.wikipedia.org/wiki/List_of_refractive_indices
https://www.sciencelearn.org.nz/resources/49-refraction-of-light
https://www.olympus-lifescience.com/en/microscope-resource/primer/lightandcolor/speedoflight/
https://www.wral.com/atmospheric-ducting-allows-us-to-see-beyond-the-horizon/17750430/
https://www.irishtimes.com/news/science/seeing-beyond-the-horizon-1.4587533