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NATURE OF LIGHT
TRANSVERSE NATURE
Fermat's principle
"Light, in going between two points, traverses
the route having the smallest optical path
length – smallest time taken."
OPD  n d
 index of refraction  distance travelled
speed of light in vacuum
c
n 

speed of light in medium  v
Huygens’ Principle
A typical statement of the principle is “every
point on a wavefront acts as a source of a
new wavefront, propagating radially
outward.”
Law of Reflection
i   r
Law of Refraction
Snell’s Law
ni sin i  nr sin r
Critical Angle
Light bends toward the normal when the light
enters a medium of greater refractive index,
and away from the normal when entering a
medium of lesser refractive index.
As you approach the critical angle the refracted
light approaches 90° and, at the critical angle,
the angle of refraction becomes 90° and the
light is no longer transmitted across the
medium/medium interface. For angles greater
in absolute value than the critical angle, all the
light is reflected. This is called total internal
reflection.
At c:
n1 sin  c  n2 sin 90
n2
sin  c 
n1
n2
 c  sin
n1
1
Fresnel's equations
describe the reflection
and transmission of
electromagnetic waves at
an interface. That is, they
give the reflection and
transmission coefficients
for waves parallel and
perpendicular to the
plane of incidence.
Reflection coefficients:
nt cos i - ni cos t
r 
ni cos t  nt cos i
tan(i - t )

tan(i  t )
ni cos i - nt cos t
r 
ni cos i  nt cos t
sin(i - t )
 sin(i  t )
Transmission coefficients:
2ni cos i
t 
ni cos t  nt cos i
2sin t cos i

sin(i  t ) cos(i  t )
2ni cos i
t 
ni cos i  nt cos t
2sin t cos i

sin(i  t )
external reflection
internal reflection
2002 Q6
a) Write down Snell's law of refraction, explaining
all the symbols you use.
b) A narrow beam of light is incident from air at an
angle of 45 degrees on a parallel-sided slab of
glass, 1-cm thick, with refractive index 1.5.
Calculate the angle of the beam inside the slab.
c) Draw a diagram showing the passage of the
light through the slab, showing clearly the angle
you have just calculated, and hence find the lateral
(perpendicular to the beam direction) shift of the
emerging beam.
2003 Q4
a) State the law of refraction (Snell's law), and
explain the terms in your equation with a diagram.
b) Light from a source in air is incident on a block
of quartz, at an angle of 40° to the normal. The
light contains two wavelengths of 405 nm and
509 nm. The indices of refraction for quartz with
respect to air at these wavelengths are 1.470 and
1.463 respectively.
Calculate the angle between the two refracted rays
in the quartz.
2005 Q11
A light bulb is set in the bottom of a 3.0-mdeep swimming pool.
What is the diameter of the circle of light
seen on the water's surface from above?
[Note that nair = 1.00 and nwater = 1.33.]
The speed of light in liquids is
a. less than in air.
b. greater than in air.
c. the same as in air.
d. zero, since particles can't move
through solids.
e. depends on the thickness of the liquid.
A monochromatic (single frequency, single
wavelength) light ray in air (n = 1) enters a glass
prism (n = 1.5). In the glass prism
a.
both the frequency and the wavelength are
the same as in air
b.
the frequency is the same, but the
wavelength is greater than in air.
c.
the frequency is the same, but the
wavelength is smaller than in air.
d.
the wavelength is the same, but the
frequency is greater than in air.
e.
the wavelength is the same, but the
frequency is smaller than in air.
The speed of light changes when it goes
from ethyl alcohol (n1 = 1.361) to carbon
tetrachloride (n2 = 1.461). The ratio of the
speeds v2/v1 is
a.
b.
c.
d.
e.
1.99
1.07
0.93
0.51
0.76
Light is refracted through a diamond. If the
angle of incidence is 30, and the angle of
refraction is 12, what is the index of
refraction?
a.
b.
c.
d.
e.
1.3
2.4
2.6
1.8
0.4
A person in a boat sees a fish in the water (n =
1.33), the light rays making an angle of 40°
relative to the water's surface. What is the true
angle (in degrees) relative to the water's surface
of the same rays when beneath the surface?
a.
b.
c.
d.
e.
40
35
50
55
61
A person looks horizontally at the edge of a
swimming pool. If its length is 5 m, and the pool is
filled to the surface, to what depth (in m) could the
observer see? (n for water is 1.33)
a. 3.2
b.4.4
c. 2.1
d.1.0
e. 0.3
A layer of ethyl alcohol (n = 1.361) is on top
of water (n = 1.333). At what angle
relative to the normal to the interface of
the two liquids is light totally reflected?
a.
b.
c.
d.
e.
78
88
68
49
the critical angle is undefined
The laws of refraction and reflection are the
same for sound as for light. The speed of
sound in air is 340 m/s and in water it is
1510 m/s. If a sound wave approaches a
plane water surface at an angle of
incidence of 12, what is the angle of
refraction?
For a light ray that is partially reflected and partially
refracted at a boundary between two media (the top
one being air), as shown in the figure, for angles of
incidence other than 0 the reflected ray is
perpendicular to the refracted ray when
a. n  tan incident
b. n  cot incident
sin incident
c. n 
sin  reflection
sin  reflection
d. n 
sin incident
e. n  sec incident