Biomedical Engineering Reference
In-Depth Information
θ
r
θ
t
θ
i
FIGURE 17.4
Ray propagation of light at the boundary of two interfaces. Clearly the angle of incidence equals
the angle of reflection (
y
i
¼ y
r
) and from Snell's law the sine of the angle of refraction bears a constant ratio to the
sine of the angle of incidence (
n
i
sin(
y
i
)
¼
n
t
sin(
y
t
)).
EXAMPLE PROBLEM 17.3
A green light beam hits the cornea of the eye, making an angle of 25 degrees with the normal,
as depicted following.
(a)
Determine the output angle from the front surface of the cornea and into the cornea, given that
the index of refraction of air is 1.000, and that of the cornea is 1.376.
(b)
What can be said about how the cornea bends the light?
Eye
1
θ
θ
2
Lens
Cornea
Solution
(a)
Snell's law, n1 sin(
y
1)
¼
n2 sin(
y
2), can be rearranged to calculate
y
2 in the lens.
sin
1
(1
y
2
¼
:
000 sin (25
Þ=
1
:
376
Þ¼
17
:
89 degrees
(b)
It has been shown and can be said that the cornea tends to bend the light toward the normal
as it passes through. This makes sense because the eye is made to bend the light so it can pass
through the center iris and lens toward the retina to be imaged by the brain.
Wave theory is used to describe the phenomena of reflection and refraction in an effort
to determine the intensity of the light as it propagates from one medium to another.
If two nonconducting media are considered, as in Figure 17.4, the boundary conditions
follow from Maxwell's equations such that
the tangential components of
E
and
H
are continuous across the boundary
E
i
þ
E
p
¼
E
t
, and the normal components of
