Biophotonics_Concepts_to_Applications

2.4.1 Snells’Law...............................

The bending or refraction of light rays at a material interface is a consequence of the
difference in the speed of light in two materials with different refractive indices. The
relationship at the interface is known asSnell’s lawand is given by

n 1 sinh 1 ¼n 2 sinh 2 ð 2 : 22 Þ

or, equivalently, as

n 1 cosu 1 ¼n 2 cosu 2 ð 2 : 23 Þ

where the angles are defined in Fig.2.9. The angleθ 1 between the incident ray and
the normal to the surface is known as theangle of incidence.
In accordance with the law of reflection, the angleθ 1 at which the incident ray
strikes the interface is the same as the angle that the reflected ray makes with the
interface. Furthermore, the incident ray, the reflected ray, and the normal to the
interface all lie in a common plane, which is perpendicular to the interface plane
between the two materials. This common plane is called theplane of incidence.
When light traveling in a certain medium reflects off of a material that has a higher
refractive index (called an optically denser material), the process is calledexternal
reflection. Conversely, the reflection of light off of a material that has a lower
refractive index and thus is less optically dense (such as light traveling in glass
being reflected at a glass–air interface) is calledinternal reflection.
As the angle of incidenceθ 1 in an optically denser material increases, the
refracted angleθ 2 approachesπ/2. Beyond this point no refraction is possible as the
incident angle increases and the light rays become totally internally reflected. The
application of Snell’s law yields the conditions required fortotal internal reflection.
Consider Fig.2.10, which shows the interface between a glass surface and air. As a

Normal

line

Reflected

ray

Material

boundary

Incident

ray

Refracted

ray

n 2 < n 1

n 1

(^11)
2
1
2
Fig. 2.9 Reflection and refraction of a light ray at a material boundary
38 2 Basic Principles of Light