1. Chapter 25 Wave Optics
Chapter 34 Opener. The beautiful colors from the surface of this soap bubble can be nicely explained by the wave theory of light. A soap bubble is a very thin spherical film filled with air. Light reflected from the outer and inner surfaces of this thin film of soapy water interferes constructively to produce the bright colors. Which colors we see at any point depends on the thickness of the soapy water film at that point and also on the viewing angle. Near the top of the bubble, we see a small black area surrounded by a silver or white area. The bubble’s thickness is smallest at that black spot, perhaps only about 30 nm thick, and is fully transparent (we see the black background). We cover fundamental aspects of the wave nature of light, including two-slit interference and interference in thin films.

2. Wave Optics studies light depend on its wave nature
properties that
depend on its wave nature
Originally, light was thought (by Newton & others) to be particles.
That model successfully explained all of geometric optics.

3. Other experiments revealed properties of light that could only be explained with
a wave theory.
Maxwell’s theory of electromagnetism convinced physicists that light was a wave.

4. Wave vs. Geometric Optics
The wavelength λ of light plays a key role in determining when geometric optics can or cannot be used.
When discussing image characteristics over distances d much greater than the wavelength, geometric optics is extremely accurate.
That is, when
d >> λ
geometric optics works very well.

5. When dealing with sizes d comparable to or smaller than the wavelength λ, wave optics is required.
That is, wave optics is needed when
d <  λ
Examples include interference effects and propagation through small openings
Later, more experiments led to the quantum theory of light (early 20th Century).
In that theory, light has properties of both
waves and particles

6. A Brief Side Note: Does light consist of waves or particles?
Modern (quantum) theory of light asks the question:
Does light consist of
waves or particles?

7. (It depends on the experiment
A Brief Side Note:
Modern (quantum) theory of light asks the question:
Does light consist of
waves or particles?
Answer:
YES!
(It depends on the experiment
& on the property)

8. Interference A property unique to waves is interference.
You might have noticed this for sound waves.
For example, interference of sound waves can be produced by two speakers as in the figure.
Interference. can be understood qualitatively by
remembering that waves are sine or cosine functions of position & time. See figure.

9. Constructive Interference
When the waves are in phase, their maxima occur at the same time at a given point in space
The total amplitude at
the listener’s location is
the sum of the
amplitudes of the two
individual waves.

10. Constructive Interference
occurs if 2 waves are in phase, so that the sum of their displacements is large
This can produce a large amplitude wave with a large intensity!

11. Destructive Interference
When the waves are out of phase, the maximum of one wave can coincide with the minimum of the other wave.
In this case, the interference is destructive.
If the waves are 180° out of phase,
the sum of the displacements of the 2 waves is zero

12. Conditions for Interference
Suppose that two or more interfering waves travel through different regions of space over at least part of their propagation from source to destination. Suppose that the waves are brought together at a common point.
Suppose that the waves have the same frequency and also have a fixed phase relationship
This means that over a given distance or time interval the phase difference between the waves remains constant
Such waves are called coherent

13. Coherence
The eye cannot follow variations of every cycle of the wave, so it averages the light intensity
For waves to interfere constructively, they must stay in phase during the time the eye is averaging the intensity
For waves to interfere destructively, they must stay out of phase during the averaging time
Both of these possibilities involve the wave having precisely the same frequency

14. Coherence
With slightly different frequencies, the interference changes from constructive to destructive and back as time goes on.
Over a large number of cycles, the waves average no interference.

15. Some Brief History: Waves vs. Particles & Huygens’ Principle
This principle states:
“Every point on a wave front
can be considered as a point
source of tiny wavelets that
spread out in the propagation
direction at the wave speed”.
Figure Huygens’ principle, used to determine wave front CD when wave front AB is given.
The overall wave front is the envelope for all of
the wavelets. That is, the wave front is tangent to
all of them. More on Huygens a little later!

16. Diffraction  The bending of a
wave around an object.
Huygens’ Principle is consistent
with diffraction.
Diffraction occurs for waves & not
particles. The fact that light exhibits
diffraction, is an indication that it
consists of waves, & not particles.
Figure Huygens’ principle is consistent with diffraction (a) around the edge of an obstacle, (b) through a large hole, (c) through a small hole whose size is on the order of the wavelength of the wave.

17. Diffraction  The bending of a wave around an object.
In Newton’s time, there were competing
theories of light. Some were based on it
being made up of particles. Others were
based on it consisting of waves.
The observation that light exhibits diffraction was considered a proof that it consists of waves & not particles.
Figure Huygens’ principle is consistent with diffraction (a) around the edge of an obstacle, (b) through a large hole, (c) through a small hole whose size is on the order of the wavelength of the wave.

18. Diffraction: Some Illustrations
around
an edge of
an obstacle
Figure Huygens’ principle is consistent with diffraction (a) around the edge of an obstacle, (b) through a large hole, (c) through a small hole whose size is on the order of the wavelength of the wave.

19. Diffraction: Some Illustrations
through a large
hole, of size
much larger
than the
wavelength.
Diffraction
around
an edge of
an obstacle
Figure Huygens’ principle is consistent with diffraction (a) around the edge of an obstacle, (b) through a large hole, (c) through a small hole whose size is on the order of the wavelength of the wave.

20. Diffraction: Some Illustrations
through a large
hole, of size
much larger
than the
wavelength.
Diffraction
through a small
hole, of similar
size to the
wavelength.
Diffraction
around
an edge of
an obstacle
Figure Huygens’ principle is consistent with diffraction (a) around the edge of an obstacle, (b) through a large hole, (c) through a small hole whose size is on the order of the wavelength of the wave.

21. Huygens’ Principle & the Law of Refraction
can be used to derive
The Law of Refraction (Snell’s Law):
As the wavelets propagate
from each point, they
propagate more slowly in the
medium of higher index of
refraction. This leads to a
bend in the wave front &
therefore in the ray.
The wave fronts are
perpendicular to
the rays.

22. sinθ1 = (v1t/AD) & sinθ2 = (v2t/AD)
Snell’s Law can be derived
using Huygens’ Principle
plus geometry & the
definition of the index of
refraction n. v  (c/n).
Speed of light in vacuum = c.
Speed of light in a medium = v.
From the figure:
sinθ1 = (v1t/AD) & sinθ2 = (v2t/AD)
or, (sinθ1/sinθ2) = (v1/v2) = (n2/n1)
or,
n1sinθ1 = n2sinθ2

23. n1sinθ1 = n2sinθ2 Figure: sinθ1 = (v1t/AD) & sinθ2 = (v2t/AD)
or, (sinθ1/sinθ2) = (v1/v2)
= (n2/n1) or,
n1sinθ1 = n2sinθ2
This has made use of the fact that, when light travels
from one medium to another, it’s frequency of does
not change, but it’s wavelength λ does: