Rule number one of perspective is that objects of the same real size, look smaller the further away they are from the viewer. Therefore a man of 6ft who is standing about 6 feet away from you, will appear to be about half his real height. If he is standing about 15 feet away, he will appear about 8 inches high. Stand him one hundred yards away and he can be hidden behind the top joint of your thumb, and so on. "
I see this sentence in a book. I don't know if the sentence here is correct. But can I still express this sentence in a function or some other way? Note : i am sorry for my english... thank you everyone
The idea is that the angle subtended by an object gets smaller the farther away it is. In the figure below
$a$ is the height of the object, $c$ is the distance to the object, and $\theta$ is the angle subtended. We have $\theta=\arctan \frac ac$. When the angle is small, $\arctan x \approx x$ so we have $\theta \approx \frac ac$. Doubling the distance cuts the angle in half. How the text converts subtended angle to apparent size is completely unclear to me.