Ruby script to calculate actual focal length at minimum focusing distance (mm) and max reproduction ratio

compute_focal_length.rb

# Pretty much all consumer lenses suffer from focus breathing at close distances, i.e the focal length changes.
# This lets us calculate the max focal length of a given lens at minimum focusing distance.
#
# Example 1: Nikon 70-200 f2.8 VR II - minimum focusing distance is 1.4m, max reproduction ratio is 0.12x.
#
#   compute_focal_length 1400, 0.12
#   => 133.92857142857142
#
# So at close distances, the Nikon isn't a 200mm lens, it's more like 135mm.
#
# Example 2: Canon 70-200 f2.8 L IS II - minimum focusing distance is 1.2m, max reproduction ratio is 0.21x.
#
#   compute_focal_length 1200, 0.21
#   => 172.11939075199783
#
# Thus, at close distances the Canon isn't 200mm either, it's more like 175mm.
#
# @param minimum_focusing_distance_mm [Numeric] minimum focusing distance in mm (so 1.4m is 1400mm)
# @param max_reproduction_ratio [Numeric] maximum reproduction ratio
#
# @return [Numeric]
def compute_focal_length(minimum_focusing_distance_mm, max_reproduction_ratio)
  nodal_point = minimum_focusing_distance_mm / (1 + 1 / max_reproduction_ratio)
  1 / ( 1 / nodal_point + 1 / (minimum_focusing_distance_mm - nodal_point) )
end