Visible Surface Area and Space Inside of the Human Eyeball

by Samuel Henry

Submitted : Spring 2019

In an eye appointment, a patient’s eyes are dilated by a medicine called Tropicamide in order to widen the pupil enough so that the optometrist can view the inside of the patient’s eye; this maximum dilation creates a circular hole with a 4 mm radius to look through.  The view of the optometrist would form the shape of a cone with a spherical cap instead of the circular, flat bottom. The surface area of the tissue of the eye visible would be the surface area of that spherical cap. The purpose of this project is to display the surface area of tissue visible and the volume of visible space inside of the eye as seperate functions of the radius of the pupil.  

This project achieved that purpose by graphing a hypothetical, circular eye at a constant distance (25 mm) from a viewpoint and graphing a line that would touch the pupil at a specific dilation (a y value of 3 meaning a dilation of 25% of the iris or a radius of 3 mm) and the viewpoint located on the x-axis.  The intersection of the circle and the line in the second quadrant would yield the height of the spherical cap and the cone, as well as the radius of the cone. This information as well as the set x value of the pupil generated enough information to calculate the volumes and surface area desired. Instead of the originally desired singular function, two solutions of functions had to be used in one function to create the equation for volume, and one solution of a function had to be used in one function to create the equation for surface area.

Related Links:

[ Back ]