Chapter Review
|
Chapter 28: Physical Optics: Interference and Diffraction Chapter Review |
|
Chapter Review
With geometrical optics most of the situations we considered were such that the wave properties of light were of little direct consequence. In this chapter we discuss aspects of the behavior of light that can only be understood in terms of its wave nature. This branch of optics is sometimes called physical optics.
28-1 Superposition and Interference
One of the key signatures of wave behavior is that of superposition, also called interference. This wave behavior for light is similar to what it is for sound waves in section 14-7. With sound, the superposition of waves occurs when different waves coexist in a region such that the net displacement at a point is the sum of the displacements of the individual waves. For light, the electric and magnetic fields play the role of the displacement. When the net fields resulting from the combination of waves have larger magnitudes than the fields from the individual waves we call this constructive interference; when the combination results in fields of reduced magnitudes we call this destructive interference.
Interference effects are noticeable when the different light waves are of the same frequency, or monochromatic, and have a constant phase relationship, or are coherent. When the phase difference between waves is 0o, or some multiple of 360o (corresponding to path differences that are multiples of the wavelength) the waves are in phase. When the phase difference is 180o, or some odd multiple of it (corresponding to path differences of odd multiples of a half wavelength) the waves are said to be completely out of phase. When the phase relationship between the different waves varies randomly, the waves are said to be incoherent.
Practice Quiz
|
|
 |
|
|
|
|
|
|
 |
28-2 Young's Two-Slit Experiment
Young's two-slit experiment is a classic experiment that demonstrates the interference properties of waves. In this experiment, monochromatic light is passed through a single slit to produce a small source of light. This light then shines on a setup containing two slits which act as independent coherent sources. By Huygen's principle we can treat each slit as a source of light spreading out in all forward directions. The light from these two slits then shines on a screen. On the screen there is a pattern of bright and dark fringes that are the result of constructive and destructive interference between the waves from the two slits.
In a typical setup the distance from the slits to the screen is much larger than the separation between the slits. This assumption simplifies the analysis. There will be constructive interference on the screen, wehre there are bright fringes, when the path difference, 
, between the light waves from the two slits equals an integral multiple of the wavelength l. Under the above assumptions, this equivalent to the condition
where q is the angle from either slit to the relevant point on the screen (which are approximately equal under the current assumptions) and d is the separation between the slits. The dark fringes result from destructive interference that occurs for path differences that are odd multiples of l/2. This leads to the condition
At the center of the interference pattern on the screen is a bright fringe. The position of a given fringe is determined by its linear distance on the screen from the center of this central bright fringe. This linear distance is given by
y = Ltanq,
where L is the distance between the screen and the plane of the two slits, and q is the angle measured from the spot exactly between the slits to the fringe being located on the screen; under the assumption that L >>d, this angle is approximately equal to the angle found from the previous two conditions for the bright and dark fringes.
Physlet Illustration: Double-Slit Interference |
||
|---|---|---|
|
|
||
| In this simulation, waves in a ripple tank originate from two small slits, shown in red. You may vary both the wavelength and the slit separation. The resulting interference may be observed in the ripples of the waves that propagate in the tank. Angles at which totally constructive interference occurs are characterized by alternating peak and troughs. Angles at which totally destructive interference occurs are characterized by an absence of such "ripples". At what angles do these interference phenomena occur? | ||
Hints:
|
Example 28.1 A Two-Slit Experiment: Light of wavelength 455 nm is incident on a two-slit apparatus with a slit separation distance of 0.125 mm? What is the distance on a screen, 2.00 m away, between the first and fifth dark fringes?
Picture the Problem The picture shows a two-slit setup and indicates the distance y between the first and fifth dark fringes.
Strategy Since we know which dark fringes we are considering we can determine their order numbers and then their angles. From that point we can calculate the difference in their linear distances on the screen.
Solution
| 1. The first dark fringe has m = +1 so its angle is: |  |
| 2. The fifth dark fringe has m = +5 so its angle is: |  |
| 3. The linear distance is determined by: | y = y5 - y1 = L[tanq5 - tanq1] |
| 4. Solving for the numerical result gives: |
Insight This problem also could have been done using m = 0 and m = -4.
Practice Quiz
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
A Pearson Company Distance Learning at Prentice Hall Legal Notice |
