Chapter 16Chapter 16

Light Waves and ColorLight Waves and Color

What causes color?

What causes reflection?

Why does a soapfilm display

differentcolors?

How do we seecolor?

Why is the skyblue?

What causes color?

What causes reflection?

What do light, radio waves,microwaves, and X rays have in

common?

a) They all can travel through empty space.b) They all travel at the same speed.c) They all have no mass.d) All the above are true.e) Only answers a and b are true.

These are all forms of electromagnetic waves.

Although seemingly quite different, they share

many properties, including a, b, and c.

Electromagnetic Waves

! An electromagnetic wave consists of time-varying electric and magnetic fields, indirections perpendicular to each other as wellas to the direction the wave is traveling.

! The electric and the magnetic fields can beproduced by charged particles." An electric field surrounds any charged particle.

" A magnetic field surrounds moving chargedparticles.

#A rapidly alternating

electric current in a wire

generates magnetic

fields whose direction

and magnitude change

with time.

#This changing

magnetic field in turn

produces a changing

electric field.

! Likewise, a changing electric field produces amagnetic field.

! Maxwell realized a wave involving these fieldscould propagate through space:" A changing magnetic field produces a changing

electric field, which produces a changing magneticfield, etc...

" Thus a transverse wave of associated changingelectric and magnetic fields is produced.

! Maxwell predicted the speed of electromagneticwaves in a vacuum using the Coulomb constant kin Coulomb’s law and the magnetic force constantk! in Ampere’s law:

! This was equal to the known value for the speed oflight!

!

v = k " k = 3#108 m s

!

c = 3"108 m s

Fizeau’s wheel for measuring the speed of light

There is a wide spectrum of

frequencies and wavelengths of

electromagnetic waves.

" Different types of electromagnetic waves havedifferent wavelengths and frequencies.

There is a wide spectrum of

frequencies and wavelengths of

electromagnetic waves.

" Together they form the electromagnetic spectrum.

There is a wide spectrum of

frequencies and wavelengths of

electromagnetic waves.

" Since they all travel at the speed of light c in avacuum, their frequencies and wavelengths arerelated by: v = c = f "

What is the frequency of radio waves with awavelength of 10 m?

" = 10 m f = v / "

v = c = 3 x 108 m/s = (3 x 108 m/s) / 10 mv = f " = 3 x 107 Hz

What is the frequency of light waves with awavelength of 6 x 10-7 m?

" = 6 x 10-7 m f = v / "

v = c = 3 x 108 m/s = (3 x 108 m/s) / 6 x 10-7 mv = f " = 5 x 1014 Hz

" Waves in different parts of the electromagneticspectrum differ not only in wavelength andfrequency but also in how they are generated andwhat materials they will travel through." Radio waves are generated by accelerated charges in an

oscillating electrical circuit.

" X rays come from energy transitions of atomic electrons.

" Gamma rays originate inside an atomic nucleus.

" Waves in different parts of the electromagneticspectrum differ not only in wavelength andfrequency but also in how they are generated andwhat materials they will travel through." Infrared light is radiated by all warm bodies.

" Oscillating atoms within the molecules of the warm bodyserve as the antennas.

" Waves in different parts of the electromagneticspectrum differ not only in wavelength andfrequency but also in how they are generated andwhat materials they will travel through." X rays will pass through materials that are opaque to

visible light.

" Radio waves will pass through walls that light cannotpenetrate.

" Different wavelengths of visible light are associatedwith different colors." Violet is about 3.8 x 10-7 m.

" Wavelengths shorter than the violet comprise ultravioletlight.

" Red is about 7.5 x 10-7 m.

" Wavelengths longer than the red comprise infrared light.

" In between, the colors are red, orange, yellow, green,blue, indigo, and violet.

Wavelength and Color

$How do we perceive ?$What causes different objects

to have

?

$Why is the sky ?

Newton demonstrated that white light

is a mixture of colors.

" He showed that white light from the sun, after being split intodifferent colors by one prism, can be recombined by asecond prism to form white light again.

How do our eyes distinguish color?

" Light is focused by the cornea and lens onto the retina.

" The retina is made up of light-sensitive cells called rods andcones.

" Three types of cones are sensitive to light in different partsof the spectrum.

$ S cones are most sensitive to shorter wavelengths.

$ M cones are most sensitive to mediumwavelengths.

$ L cones are most sensitive to longer wavelengths.

$ The sensitivity ranges overlap, so that light near themiddle of the visible spectrum will stimulate all threecone types.

#Light of 650 nm

wavelength stimulates L

cones strongest and S

cones weakest; the brain

identifies the color red.

$ S cones are most sensitive to shorter wavelengths.

$ M cones are most sensitive to mediumwavelengths.

$ L cones are most sensitive to longer wavelengths.

$ The sensitivity ranges overlap, so that light near themiddle of the visible spectrum will stimulate all threecone types.

#Light of 450 nm

stimulates the S cones

most strongly, and the

brain interprets that as the

color blue.

$ S cones are most sensitive to shorter wavelengths.

$ M cones are most sensitive to mediumwavelengths.

$ L cones are most sensitive to longer wavelengths.

$ The sensitivity ranges overlap, so that light near themiddle of the visible spectrum will stimulate all threecone types.

#Light of 580 nm

stimulates both the M and

L cones strongly, and the

brain identifies that as the

color yellow.

#A mixture of red and

green light will produce a

similar response.

Color Mixing

! The process of mixing two differentwavelengths of light, such as red and green, toproduce a response interpreted as anothercolor, such as yellow, is additive color mixing.

#Combining the three primary colors

blue, green, and red in different

amounts can produce responses in

our brains corresponding to all the

colors we are used to identifying.

#Red and green make yellow, blue

and green make cyan, and blue and

red make magenta.

#Combining all three colors

produces white.

Color Mixing

! The pigments used in paints or dyes work byselective color mixing." They absorb some wavelengths of light more than

others.

#When light strikes an

object, some of the light

undergoes specular

reflection: all the light is

reflected as if by a

mirror.

Color Mixing

! The pigments used in paints or dyes work byselective color mixing." They absorb some wavelengths of light more than

others.

#The rest of the light

undergoes diffuse

reflection: it is reflected in

all directions.

#Some of the light may be

selectively absorbed,

affecting the color we see.

#If red light is absorbed,

we see blue-green.

Color Mixing

! The selective absorption of light is a form ofsubtractive color mixing." In color printing, the three primary pigments are

cyan, yellow, and magenta.

#Cyan absorbs red but transmits and

reflects blue and green.

#Yellow absorbs blue but transmits and

reflects green and red.

#Magenta absorbs at intermediate

wavelengths, but transmits and reflects

blue and red.

Color Mixing

! The selective absorption of light is a form ofsubtractive color mixing." In color printing, the three primary pigments are

cyan, yellow, and magenta.

#Cyan mixed with yellow absorb blue

and red, resulting in green.

#Cyan and magenta produce blue.

#Yellow and magenta produce red.

#These resulting colors are the primary

colors for additive color mixing.

Why is the sky blue?

#The white light coming from the sun is actually a mixture of light ofdifferent wavelengths (colors).#The longer wavelengths of blue light are scattered by gas moleculesin the atmosphere more than shorter wavelengths such as red light.#The blue light enters our eyes after being scattered multiple times,so appears to come from all parts of the sky.

Why is the sunset red?

#The shorter wavelengths of blue light are scattered by gas moleculesin the atmosphere more than longer wavelengths such as red light.#When the sun is low on the horizon, the light must pass through moreatmosphere than when the sun is directly above.#By the time the sun’s light reaches our eyes, the shorter wavelengthssuch as blue and yellow have been removed by scattering, leaving onlyorange and red light coming straight from the sun.

Interference of Light

Waves$ Is light a wave or a particle?

" If it is a wave, it should exhibit interference effects:

Recall thattwo waves can

interfereconstructively

ordestructivelydepending ontheir phase.

#Light from a single slit is split by passing through two slits,

resulting in two light waves in phase with each other.

#The two waves will interfere constructively or destructively,

depending on a difference in the path length.

#If the two waves travel equal distances to the screen, they

interfere constructively and a bright spot or line is seen.

#If the distances traveled differ by half a wavelength, the two

waves interfere destructively and a dark spot or line appears

on the screen.

#If the distances traveled differ by a full wavelength, the two

waves interfere constructively again resulting in another

bright spot or line.

#The resulting interference pattern of alternating bright and

dark lines is a fringe pattern.

!

path difference = dy

x

Red light with a wavelength of 630 nm strikes a double slitwith a spacing of 0.5 mm. If the interference pattern is

observed on a screen located 1 m from the double slit, how farfrom the center of the screen is the second bright line from

the central (zenith) bright line?

!= 630 nm = 6.3 x 10-7 m

d = 0.5 mm = 5 x 10-4 m

x = 1 m

!

path difference = 2" = dy

x

y =2"x

d=

2 6.3#10$7 m( ) 1 m( )

5 #10-4 m( )= 0.0025 m = 2.5 mm

! Similarly, interference can occur when light wavesare reflected from the top and bottom surfaces of asoap film or oil slick.

! The difference in the path length of the two wavescan produce an interference pattern.

! This is calledthin-filminterference.

! Different wavelengths of light interfere constructivelyor destructively as the thickness of the film varies.

! This results in the many different colors seen.

! The thin film may also be air between two glass plates.

! Each band represents a different thickness of film.

Diffraction and Gratings

! The bright fringes in a double-slit interferencepattern are not all equally bright." They become less bright farther from the center.

" They seem to fade in and out.

! This effect, called diffraction, is due tointerference of light coming from differentparts of the same slit or opening.

#When the path difference between light coming from the top

half of the slit and that coming from the bottom half is 1/2 of a

wavelength, a dark line appears on the single-slit diffraction

pattern.

#The position of the first dark fringe is:

!

y ="x

w

Light with a wavelength of 550 nm strikes a single slit that is0.4 mm wide. The diffraction pattern produced is observed ona wall a distance of 3.0 m from the slit. What is the distance

from the center of the pattern to the first dark fringe?

!

y ="x

w=

5.5 #10$7

m( ) 3.0 m( )

0.4 #10-3

m( )= 0.0041 m = 4.1 mm

!= 550 nm = 5.5 x 10-7 m

w = 0.4 mm = 4 x 10-4 m

x = 3.0 m

How wide is the central bright fringe of this diffractionpattern?

!

2y = 2 4.1 mm( ) = 8.2 mm

!= 550 nm = 5.5 x 10-7 m

w = 0.4 mm = 4 x 10-4 m

x = 3.0 m

The central bright fringe extends out to the first dark fringeon either side, so its width is just twice the distance y:

! The diffraction pattern produced by a square openinghas an array of bright spots.

! Looking at a star or distant street light through awindow screen can produce a similar diffractionpattern.

! A diffraction grating has a very large number of slits veryclosely spaced.

! Whenever the path difference is equal to an integer multiple ofthe light wavelength,we get a strong bright fringe forthat wavelength.

! Different wavelengths will appear at different points on thescreen, spreading the light into its spectrum.

! Diffraction gratings in spectrometers are used to separate andmeasure the wavelengths of light.

! Gratings also produce the effects seen in novelty glasses,reflective gift wrappings, and in the colors seen on a CD.

!

dy

x= m", m = 0,±1,±2,...

Polarized Light

$ How do polarizing sunglasses and camerafilters work?

$ What is polarized light?

#Recall that light is an electromagnetic wave consisting of

oscillating electric and magnetic fields:

! The oscillating electric field vector shown is in thevertical plane, and the magnetic field is horizontal.

! Actually, the electric field could oscillate in thehorizontal with the magnetic field in the vertical plane,or the electric field could oscillate at some angle to thehorizontal.

! As long as the electric field is always pointing in thesame direction for all the waves, the light is polarized.

! The electric field vector oscillates in a singledirection for polarized light.

! Unpolarized light has random directions oforientation.

#Light is usually

produced

unpolarized.

#To make light

polarized,

something must

occur to select just

one direction of

field oscillation.

! Polarizing filters allows only that componentof each electric field vector that is aligned withthe filter’s axis of transmission to passthrough.

#The component

perpendicular to

this axis is

absorbed.

! Reflection from a smooth surface of atransparent material such as glass or watercan also polarize light.

#Incoming sunlight isunpolarized.

#When the anglebetween the reflectedwave and thetransmitted wave is aright angle, the reflectedwave is polarized.

#Polarizing sunglassescan help reduce glarefrom reflected sunlight.

! Many interesting and colorful effects arerelated to the phenomenon of birefringence." Birefringence is also called double refraction.

" Light with different polarizations travels withdifferent velocities when passing through abirefringent material.

" This causes colorful displays when the birefringentmaterial is viewed through crossed polarizers.

#Calcite crystals area good example ofbirefringent material.

#Lines are doubledwhen viewedthrough a calcitecrystal.

! Many interesting and colorful effects arerelated to the phenomenon of birefringence." Birefringence is also called double refraction.

" Light with different polarizations travels withdifferent velocities when passing through abirefringent material.

" This causes colorful displays when the birefringentmaterial is viewed through crossed polarizers.

#A plastic lens undercompression showsstress birefringencewhen viewedbetween crossedpolarizers.