There are 360 degrees in a circle
There are 2pi radians in a circle
one degree is equal to 17.45 milliradians
one arc-minute is 1/60 degrees
one arc-second is 1/60 arc-minute, or 1/3600 degrees
one arc-second is 4.85 microradians
small angle approximation (works when using radians, milliradians or microradians)
the sine of the angle theta is approximately equal to theta if theta is less than a few degrees
sin(theta) ~= theta [radians]
Add a graph here to show this!
So, to figure a telescope field of view (which is small) divide the width of the field by the range to the field, and you have the FOV in radians. That is why radians are so useful.
There are 2pi radians in a circle
one degree is equal to 17.45 milliradians
one arc-minute is 1/60 degrees
one arc-second is 1/60 arc-minute, or 1/3600 degrees
one arc-second is 4.85 microradians
small angle approximation (works when using radians, milliradians or microradians)
the sine of the angle theta is approximately equal to theta if theta is less than a few degrees
sin(theta) ~= theta [radians]
Add a graph here to show this!
So, to figure a telescope field of view (which is small) divide the width of the field by the range to the field, and you have the FOV in radians. That is why radians are so useful.