If i'm standing on the sand, how far into the ocean can i see?

Question

we are trying to figure out how many miles into the ocean we can see while standing on the sand

Answer 1

Let R = radius of Earth, h = height of eyes, and x = distance to the horizon.  Then we have, by Pythagorean:

R² + x²  = (R + h)² = R² + 2Rh + h²

x = √(2Rh + h²)

If we eliminate h² because it's very small compared to 2Rh, we have:

x = √(2Rh)

If R = 4,000 miles, and h = 5/(5,280) miles, or roughly 1/(1,000) miles, we have:

x = √((2)(4000)(1/1000)) = 2√2, or roughly 2.8 miles.  Not very far, isn't it?  It is for this reason that ancient seafarers were able to discern distant ships "sinking below the horizon", and thus were able to correctly deduce that the Earth was round.  It is a myth that they all thought that the world was flat.

Answer 2

as I remember , if the visibility is clear , we can see an object 60-80 meters = ? miles ( I can't remember how to translate meter into mile , hihihihi)

Answer 3

About 30 miles depending on the weather conditions and the position of the sun.  Also, a person's height increases the distance.  If your talking about looking down into the water, that would depend on how murky the water is.