Diopters

An equation like d _i=1/θ_i really doesn't make sense in terms of units. Angles are unitless, since radians aren't really units, so the right-hand side is unitless. We can't have a left-hand side with units of distance if the right-hand side of the same equation is unitless. This is an artifact of our cavalier statement that our conical bundles of rays spread out to a distance of 1 from the axis where they strike the mirror, without specifying the units used to measure this 1. In real life, optometrists define the thing we're calling θ_i=1/d _i as the "dioptric strength" of a lens or mirror, and measure it in units of inverse meters (m^-1), also known as diopters (1D = 1m^-1).