Chapter 27 Interference and the Wave Nature of Light.

Chapter 27

Interference and the Wave Nature of Light

27.1 The Principle of Linear Superposition

When two or more light waves pass through a given point, their electricfields combine according to the principle of superposition.

The waves emitted by the sources start out in phase and arrive at point P in phase, leading to constructive interference.

,3,2,1,0 12 mm


The waves emitted by the sources start out in phase and arrive at point P out of phase, leading to destructive interference.

,3,2,1,0 21

12 mm


If constructive or destructive interference is to continue ocurring at a point, the sources of the waves must be coherent sources.

Two sources are coherent if the waves they emit maintain a constantphase relation.

27.2 Young’s Double Slit Experiment

In Young’s experiment, two slits acts as coherent sourcesof light.

Light waves from these slits interfere constructively anddestructively on the screen.


The waves coming from the slits interfere constructively ordestructively, depending on the difference in distances betweenthe slits and the screen.



sind

Bright fringes of a double-slit

Dark fringes of a double-slit

,3,2,1,0 sin md

m

,3,2,1,0 sin 21 md

m


Example 1 Young’s Double-Slit Experiment

Red light (664 nm) is used in Young’s experiment with slits separatedby 0.000120 m. The screen is located a distance 2.75 m from the slits.Find the distance on the screen between the central bright fringe andthe third-order bright fringe.


951.0m101.20

m106643sinsin

4

911

dm

m 0456.0951.0tanm 75.2tan Ly


Conceptual Example 2 White Light and Young’s Experiment

The figure shows a photograph that illustrates the kind of interferencefringes that can result when white light is used in Young’s experiment.Why does Young’s experiment separate white light into its constituent colors? In any group of colored fringes, such as the two singled out, why is red farther out from the central fringe than green is? Why isthe central fringe white?

27.3 Thin Film Interference

Because of reflection and refraction,two light waves enter the eye when lightshines on a thin film of gasoline floating on a thick layer of water.

Because of the extra distance traveled, therecan be interference between the two waves.

nvacuum

film


When light travels through a material witha smaller refractive index towards a materialwith a larger refractive index, reflection atthe boundary occurs along with a phasechange that is equivalent to one-half ofa wavelength in the film.

When light travels from a larger towards a smaller refractive index, there is no phasechange upon reflection.


Example 3 A Colored Thin Film of Gasoline

A thin film of gasoline floats on a puddle of water. Sunlight falls perpendicularly on the film and reflects into your eyes. The film hasa yellow hue because destructive interference eliminates the colorof blue (469 nm) from the reflected light. The refractive indices of theblue light in gasoline and water are 1.40 and 1.33. Determine the minimum non-zero thickness of the film.


film25

film23

film21

film21 ,,2 t

2filmm

t

nm 168

2

1.40nm 4691

2film

mt


The wedge of air formed between two glass platescauses an interferencepatter of alternating darkand bright fringes.

Example• a) Assuming that green light

(λvacuum = 552 nm) strikes the glass plates nearly perpendicularly determine the number of bright fringes that occur between the place where the plates touch and the edge of the sheet of paper (thickness = 4.10 × 10–5 m). (b) Explain why there is a dark fringe where the plates touch

Solution• a-

Since the first bright fringe occurs when m = 0, the number of bright fringes is m+1=149

Part b

• b) Where the plates touch, there is a dark fringe because of destructive interference between the light waves represented by rays 1 and 2. Destructive interference occurs because the thickness of the wedge is zero here and the only difference between the rays is the half-wavelength phase change due to reflection from the lower plate.

Circular interference fringes

• The air wedge between a convex spherical glass surface and an optically flat plate leads to a pattern of circular interference fringes that is known as Newton’s rings.

The Michelson Interferometer

• An interferometer is an apparatus that can be used to measure the wavelength of light by utilizing interference between two light waves

27.5 Diffraction

Diffraction is the bending of waves aroundobstacles or the edges of an opening.

Huygens’ principle

Every point on a wave front acts as a sourceof tiny wavelets that move forward with the samespeed as the wave; the wave front at a latterinstant is the surface that is tangent to thewavelets.

27.5 Diffraction

The extent of the diffraction increases as the ratio of the wavelengthto the width of the opening increases.

27.5 Diffraction

27.5 Diffraction

This top view shows five sources of Huygens’ wavelets.

27.5 Diffraction

These drawings show how destructiveinterference leads to the first dark fringeon either side of the central bright fringe.

27.5 Diffraction

Dark fringes forsingle slitdiffraction

,3,2,1 sin mW

m

27.5 Diffraction

27.6 Resolving Power

First minimum of a circular diffraction pattern

D

22.1sin

diameter of hole



Rayleigh criterion

Two point objects are just resolved when the first dark fringe inthe diffraction pattern of one falls directly on the central bright fringe in the diffraction patter of the other.

D

22.1min

The Diffraction Grating

• Diffraction patterns of bright and dark fringes occur when monochromatic light passes through a single or double slit. Fringe patterns also result when light passes through more than two slits, and an arrangement consisting of a large number of parallel, closely spaced slits called a diffraction grating

27.7 The Diffraction Grating

The conditions shown here lead to the first- and second-order intensitymaxima in the diffraction pattern.


The bright fringes produced bya diffraction grating are much narrower than those produced bya double slit.

Principal maxima of adiffraction grating

,3,2,1,0 sin md

m

distance betweenslits


Example 9 Separating Colors With a Diffraction Grating

A mixture of violet (410 nm) light and red (660 nm) light falls ontoa grating that contains 1.0x104 lines/cm. For each wavelength,find the angle that locates the first-order maximum.


24m101.0

m10410sinsin

6

91violet1

d

41m101.0

m10660sinsin

6

91red1

d

27.8 Compact Discs, Digital Video Discs, and the Use of Interference

27.8 Compact Discs, Digital Video Discs, and the Use of Interference

27.9 X-Ray Diffraction

27.9 X-Ray Diffraction

Chapter 27 Interference and the Wave Nature of Light.

Documents

light waves

youngs experiment

doubleslit slide

blue light

light travels

coherent sources of

light shines

reflected light