Calculating camera angle of view

Question

I know the formula to calculate a camera's angle of view given the film size and the focus distance. I.e., 35mm film at 50mm focal length. It works just fine returning the AOV.

Formula in python:

d = 35 # Film Width
f = 50 # Focal Length
aov = 2 * math.atan(float(d) / (2*float(f)))

which results in an AOV of 38.58

My question is how would I calculate the Focal Length f given the film size d and the aov?

Answer 1

You can calculate the focal length with:

f = d / (2 * math.tan(0.5 * aov))

This is derived from the theorem of intersecting lines and the tangents in right-angled triangles:

(0.5 * d)/f = a/b = tan(0.5 * aov)