In order to model how
light rays bend and refract in our eyes, we can perform step-by-step ray
tracing. In this section, I'll attempt to explain how these pictures
were modelled by going through the step-by-step ray tracing method.

Snell's Law and Refraction

When dealing with
light and refraction, the basic physical law that we appeal to is
Snell's Law. Snell's Law relates the incoming angle of the light ray
with its new refracted angle once it goes into another medium:

n_{i} sin i = n_{r} sin
r

where:

n

i = the incident angle (in degrees)

n

r = the refracted angle (in degrees)

This diagram below
sketches a picture of the system that we are looking at. Notice
that the angle of incidence and refraction are both relative to the
line perpendicular (or normal) to the surface (the dashed line). The solid black line
represents the ray of light as it strikes the grey shaded lens. The
refracted ray is coloured blue, and the green line represents the ray of
light if it has travelled straight through without being changed. As you
can see, the ray of line bends "inward" towards the normal, and angle r is smaller than i is. This is a general behaviour of
lens which have this convex shape. It turns out that concave lens have
the reverse property; when going into materials with higher indices of
refraction, convex lens tend to bend outward.

When tracing the ray through the
different interfaces, the same fomula is used over and over again. This
generates the pictures as they were used in the project.

Lens Shapes

In order to simplfy the calculations
for this project, the lens that were used (both the eye and the
corrective lens) are assumed to be spherical. A spherical lens is formed
in the following way:

The lens has two surfaces, both of which
can be approximated as being the soild that results from the
intersection of two spheres. The two intersecting spheres, with radii R
and R' have two centers located at C and C' respectively. In the next
section, we will discuss how variations in the distance between C and C'
effect the distance, d, and the effect it has on lens focusing.

Introduction

Colour Vision

Colour Math

Approximations

Focal Lengths and Distances

GRIN Systems

Human Vision

Vision Problems

Corrections

Introduction

Colour Vision

Colour Math

Approximations

Focal Lengths and Distances

GRIN Systems

Human Vision

Vision Problems

Corrections