Chapter 35 The Nature of Light

and the Principle of

Ray Optics

普通物理(二)
國立交通大學 電子物理系
授課老師：羅志偉
Chapter Outline
 35.1 The Nature of Light
 35.2 Measurements of the Speed of Light
 35.3 The Ray Approximation in Ray Optics
 35.4 Analysis Model: Wave Under Reflection
 35.5 Analysis Model: Wave Under Refraction
 35.6 Huygens’s Principle
 35.7 Dispersion
 35.8 Total Internal Reflection
 35-1 The Nature of Light
A Dual Nature
Particle Nature Wave Nature
In ~1887 In 1801
Heinrich Rudolf Hertz Thomas Young (1773-
(1857 - 1894) 1829)
 Photoelectric effect  Interference

In 1900
In 1873
Max Planck (1858-1947)
James Clerk Maxwell
 Planck constant (1831-1879)
Isaac Newton Christian Huygens
h = 6.63 × 10-34 J ⋅ s (1629 -1695)  Electromagnetic wave
(1642 -1727)
English physicist Dutch physicist
& Mathematician In 1905 & Astronomer In 1887
Albert Einstein (1879- Heinrich Rudolf Hertz
1955) (1857 - 1894)
 Photon E = hf  Confirmed EM wave
35-2 Measurements of the Speed of
Light
In 1667, Galileo: at least 10 times faster than sound.

Roemer’s Method (In 1675, Danish) Fizeau’s Method (In 1849, French)
Using Roemer’s data, Huygens estimated d is the distance between the wheel and
the lower limit of the speed of light to be the mirror. ∆t is the time for one round
2.3×108 m/s. trip. Then c = 2d/∆t
Fizeau found a value of c = 3.1×108 m/s.

This was important because it demonstrated

that light has a finite speed as well as
giving an estimate of that speed.
35-3 The Ray Approximation in Ray
Optics
 Ray optics (sometimes called geometric optics)
involves the study of the propagation of light.

 It uses the assumption that light travels in a straight-line

path in a uniform medium and changes its direction when
it meets the surface of a different medium or if the optical
properties of the medium are nonuniform.

 The ray approximation is used to represent beams of light.

35-4 Analysis Model: Wave Under
Reflection
Specular Reflection Law of Reflection
 The incident ray,
the reflected ray
and the normal are
all in the same
plane.

θ′1 = θ1

Diffuse Reflection
Retroreflection
35-5 Analysis Model: Wave Under
Refraction
Refraction
The ray that enters the second medium changes its
direction of propagation at the boundary.

The angle of refraction depends upon the material

and the angle of incidence.
sin θ 2 v2 v1 is the speed of the light in the first medium and
= v2 is its speed in the second.
sin θ1 v1

Light in a Medium
The electron in medium
may absorb the light,
oscillate, and reradiate
the light. The absorption
and radiation cause the
decrease of average
speed of the light.
35-5 Analysis Model: Wave Under
Refraction
Index of Refraction
 The speed of light in any material is less than its speed in vacuum.
 The index of refraction, n, of a medium can be defined as
speed of light in a vacuum c
n≡ ≡
speed of light in a medium v
 The frequency stays the same as the wave
travels from one medium to the other.
 f1 = f2 but v1 ≠ v2 (v = f λ) so λ1 ≠ λ2
The ratio of the indices of refraction of the two
media can be expressed as various ratios.
λ1 v1 c / n1 n2
= = = ⇒ λ1n1 = λ2n2
λ2 v2 c / n2 n1
sin θ 2 v2
 = n1 sin θ1 = n2 sin θ 2 Snell’s law of refraction
sin θ1 v1
 35-5 Analysis Model: Wave Under
Refraction
Example 35.1: A light beam passes from medium l to medium 2, with
the latter medium being a thick slab of material whose index of refraction is n2.
Show that the beam emerging into medium l from the other side is parallel to
the incident beam.
Solution

n1
(1) sin θ 2 = sin θ1
n2
n2
(2) sin θ3 = sin θ 2
n1
n2  n1 
=sin θ3 =  sin θ1  sin θ1
n1  n2 
35-5 Analysis Model: Wave Under
Refraction
Example 35.2: Although we do not prove it here, the min. angle of
deviation δmin for a prism occurs when the angle of incidence θ1 is such that
the refracted ray inside the prism makes the same angle with the normal to
the two prism faces. Obtain an expression for the index of refraction of the
prism material in terms of the min. angle of deviation and the apex angle Φ.

Solution
Φ δ min Φ + δ min
θ1 = θ 2 + α = + =
2 2 2
sin θ1
=
(1.00) sin θ1 n sin θ 2 →
= n
sin θ 2
 Φ + δ min 
sin  
n=  2 
sin(Φ / 2)
35-6 Huygens’s Principle
All points on a given wave front are taken as point
sources for the production of spherical secondary waves,
called wavelets, which propagate outward through a
medium with speeds characteristic of waves in that
medium. After some time has passed, the new position
of the wave front is the surface tangent to the wavelets.

For Reflection For Refraction

BC AD BC v1Δt AD v2Δt
cos γ = and cos γ ′ = sinθ1 = = and sinθ 2 = =
AC AC AC AC AC AC
 AD = BC sin θ1 v1
⇒ =
∴ cos γ = cos γ ′ sin θ 2 v2
⇒γ =γ′ =
c / n1 n2
=
⇒ 90o − θ1 = 90o − θ1′ c / n2 n1
θ1 = θ1′ n1 sin θ1 = n2 sin θ 2
35-7 Dispersion
For a given material, the index of refraction varies with
the wavelength of the light passing through the material.
This dependence of n on λ is called dispersion.

∵Snell’s law of refraction n1 sin θ1 = n2 sin θ 2

The Rainbow
35-8 Total Internal Reflection
Critical Angle Optical Fibers
 n1 sin θ1 = n2 sin θ 2 when θ1 = θ c , θ 2 = 90o

n1 sin θ c = n2 sin 90o = n2

n2
sin θ c = (for n1 > n2 )
n1
Summary
 The dual nature of Light: Particle & Wave

speed of light in a vacuum c

 Index of refraction: n ≡ ≡
speed of light in a medium v

 The Ray Approximation in Ray Optics

sin θ 2 v2
 Refraction = n1 sin θ1 = n2 sin θ 2
sin θ1 v1

 Huygens’s Principle

n2
 Total Internal Reflection sin θ c =
n1