PHYSICS

21.2.2. Laws of Geometric Optics
sin e = n 2
( - n 1
(21.4)
Law of Reflection: When a ray of light is reflected from a plane
surface, the incident ray and the reflected ray all lie in the same
plane; the angle of reflection equals the angle of incidence:
i=r
(21.1)
Law of Refraction: When a ray of light passes from one medium
to another, the incident ray, the reflected ray, and the refracted ray
all lie in the same plane; the sine of the angle of incidence bears a
constant ratio to the sine of the angle of refraction:
sin i / sin r = n
( 21.2 )
t
where n I is greater than n2"
2 1
n 2
Fig. 21.4. Total internal reflection
For angles of incidence
greater than i,
the beam is entirely reflected
at the boundary. In
such a way, total internal
reflection occurs only
when light attempts to move
from a medium ofgiven
index of refraction to
a medium of lower index
of refraction.
The ratio sin i / sin r is known as the refractive index from one
medium to another. It is convenient to define the refractive index
of a medium to be the ratio:
c
n=­
V
(21.3 )
where c is the speed of light in a vacuum and, V ­ the speed of
light in a medium.
Here are refraction index values for several common materials
are: air = 1.0003, water = 1.33, glass = 1.52, diamond = 2.42,
lead sulfide = 3.91.
21.2.3. Total Internal Reflection
An interesting effect, called total internal reflection, can occur
when light attempts to move from a medium having given index
of refraction (n) to one having a lower index of refraction (n)
(fig. 21.4). All possible directions of the beam are indicated by rays
1 through 5. At some particular angle of incidence, (i), called
the critical angle, the refracted light ray will move parallel to the
boundary. The value of the critical angle (8) can be found from
the following expression:
142
, ;~
,
Example. Find the critical angle for a water-air boundary (a view from
the fish's eye) if the index of refraction of water is \.33.
Solution. Applying the equation (2\.4), we find the critical angle
to be sine 0= n 1 =_1_ =0 752
c n, 1.33 .
Optical fibers are devices that can be used for transporting
radiation from the source to the sample (e.g., a biological tissue)
for diagnostics, therapy, or surgery. An optical fiber consists of a
long, thin and flexible rod of transparent material. The principle
of the operation of a fiber is based on total internal reflection
that depends on the angle of incidence of the light ray and the
refractive index of the fiber (fig. 21.5). Usually, each fiber consists
three parts: the core at the centre of the fiber; a concentric
Cladding
8 c
= 48.8"
21.2.4. Fiber Optics
... --~--
-----­
Fig. 21.5. Principle
of operation of fiber
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