Refraction as an explanation for light curvature

[omrit]

Wikipedia states that:
"If the measurement is close enough to the surface, light rays can curve downward at a rate equal to the mean curvature of the Earth's surface. In this case, the two effects of assumed curvature and refraction could cancel each other out and the Earth will appear flat in optical experiments."

My question is -- why would the light curve necessarily downward, and why would it curve at the rate equal to the mean curvature of the Earth?

 

[jbriggs444]

Wikipedia states that:
"If the measurement is close enough to the surface, light rays can curve downward at a rate equal to the mean curvature of the Earth's surface. In this case, the two effects of assumed curvature and refraction could cancel each other out and the Earth will appear flat in optical experiments."

My question is -- why would the light curve necessarily downward, and why would it curve at the rate equal to the mean curvature of the Earth?

Do you have a reference more specific than "wikipedia says"? The article at https://en.wikipedia.org/wiki/Atmospheric_refraction does not say such a thing.

The density gradient of air means that, if all other things are equal, light travels more slowly near the surface where the atmosphere is most dense. That causes a downward curve. If that downward curvature were greater than or equal to the curvature of the Earth's surface then we would not see the sun set (we would, instead, expect to see it fade out to an orange glow and then to nothing as the viewing path through the atmosphere becomes longer and longer).

 

[omrit]

Thanks. The Wikipedia entry I took this from is: https://en.wikipedia.org/wiki/Bedford_Level_experiment
It claims that this effect (light rays curving downward at a rate equal to the mean curvature of the Earth's surface) can "explain" why long water stretches (like in the Bedford Level experiment) seem flat, rather than taking the curvature of the Earth. So I understand from your reply that you disagree?

 

[jbriggs444]

Thanks. The Wikipedia entry I took this from is: https://en.wikipedia.org/wiki/Bedford_Level_experiment
It claims that this effect (light rays curving downward at a rate equal to the mean curvature of the Earth's surface) can "explain" why long water stretches (like in the Bedford Level experiment) seem flat, rather than taking the curvature of the Earth. So I understand from your reply that you disagree?

I disagree with a claim that atmospheric refraction is, on average, equal to the curvature of the Earth at sufficiently low altitudes and viewing angles. However, that is not a claim that is made on the page in question.

If you chase the refererence from Wiki, it is to a document on celestial navigation. That document does not support a claim that atmospheric refraction is, on average, equal to the curvature of the Earth at sufficiently low viewing angles. At various places, it does point out that the effects of refraction are most erratic at low angles.

On close reading, the Wiki page that you point to explaining the negative result of the Bedford Level experiment also does not quite claim that atmospheric refraction is, on average, equal to the curvature of the Earth at sufficiently low viewing angles. It only claims that refraction can attain such rates of curvature.