I have a castle in my book that can see a distant land as only a tiny grey line over a vast ocean.

The ocean is called the Far Sea and I imagine it being maybe 100 miles between the northern shore and the southern shore where this castle is.

I'm no mathematician soooooo... I have two questions:

1.) How high up would this castle have to be in order to see this land as merely a thin grey line?

2.) I'm envisioning this castle to be maybe 1000-1500 feet above sea level. What is the furthest possible point they could see on the horizon (in miles not feet)