Chapter 1.2, Problem 73E

Relative acuity of the human eye The fovea centralis (or fovea) is responsible for the sharp central vision that humans use for reading and other detail-oriented eyesight. The relative acuity of a human eye, which measures the sharpness of vision, is modeled by the function

$R(\theta )=\frac{0.568}{0.331\left|\theta \right|+0.568’}$

where θ (in degrees) is the angular deviation of the line of sight from the center of the fovea (see figure).

1. a. Graph R, for −15 ≤ θ ≤ 15.
2. b. For what value of θ is R maximized? What does this fact indicate about our eyesight?
3. c. For what values of θ do we maintain at least 90% of our maximum relative acuity? (Source: The Journal of Experimental Biology, 203, Dec 2000)