Chapter 16 Light Waves and Color
What causes color? What causes reflection?
What causes color? What causes reflection? Why does a soap film display different colors? How do we see color? Why is the sky blue?
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 timevarying electric and magnetic fields, in directions perpendicular to each other as well as to the direction the wave is traveling.
! The electric and the magnetic fields can be produced by charged particles. " An electric field surrounds any charged particle. " A magnetic field surrounds moving charged particles. #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 a magnetic field.! Maxwell realized a wave involving these fields could propagate through space: " A changing magnetic field produces a changing electric field, which produces a changing magnetic field, etc... " Thus a transverse wave of associated changing electric and magnetic fields is produced.
! Maxwell predicted the speed of electromagnetic waves in a vacuum using the Coulomb constant k in Coulomb s law and the magnetic force constant k! in Ampere s law: v = k k " = 3 #10 8 m s! This was equal to the known value for the speed of light! c = 3"10 8 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 have different 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 a vacuum, their frequencies and wavelengths are related by: v = c = f "
What is the frequency of radio waves with a wavelength of 10 m? " = 10 m f = v / " v = c = 3 x 10 8 m/s = (3 x 10 8 m/s) / 10 m v = f " = 3 x 10 7 Hz
What is the frequency of light waves with a wavelength of 6 x 10-7 m? " = 6 x 10-7 m f = v / " v = c = 3 x 10 8 m/s = (3 x 10 8 m/s) / 6 x 10-7 m v = f " = 5 x 10 14 Hz
" Waves in different parts of the electromagnetic spectrum differ not only in wavelength and frequency but also in how they are generated and what 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 electromagnetic spectrum differ not only in wavelength and frequency but also in how they are generated and what materials they will travel through. " Infrared light is radiated by all warm bodies. " Oscillating atoms within the molecules of the warm body serve as the antennas.
" Waves in different parts of the electromagnetic spectrum differ not only in wavelength and frequency but also in how they are generated and what 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 cannot penetrate.
" Different wavelengths of visible light are associated with different colors. " Violet is about 3.8 x 10-7 m. " Wavelengths shorter than the violet comprise ultraviolet light. " 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 into different colors by one prism, can be recombined by a second 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 and cones. " Three types of cones are sensitive to light in different parts of the spectrum.
$ S cones are most sensitive to shorter wavelengths. $ M cones are most sensitive to medium wavelengths. $ L cones are most sensitive to longer wavelengths. $ The sensitivity ranges overlap, so that light near the middle of the visible spectrum will stimulate all three cone 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 medium wavelengths. $ L cones are most sensitive to longer wavelengths. $ The sensitivity ranges overlap, so that light near the middle of the visible spectrum will stimulate all three cone 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 medium wavelengths. $ L cones are most sensitive to longer wavelengths. $ The sensitivity ranges overlap, so that light near the middle of the visible spectrum will stimulate all three cone 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 different wavelengths of light, such as red and green, to produce a response interpreted as another color, 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 by selective 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 by selective 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 of subtractive 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 of subtractive 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 of different wavelengths (colors). #The longer wavelengths of blue light are scattered by gas molecules in 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 molecules in the atmosphere more than longer wavelengths such as red light. #When the sun is low on the horizon, the light must pass through more atmosphere than when the sun is directly above. #By the time the sun s light reaches our eyes, the shorter wavelengths such as blue and yellow have been removed by scattering, leaving only orange 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 that two waves can interfere constructively or destructively depending on their 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 = d y x
Red light with a wavelength of 630 nm strikes a double slit with a spacing of 0.5 mm. If the interference pattern is observed on a screen located 1 m from the double slit, how far from 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" = d y x y = 2"x d ( ) 1 m ( ) 2 6.3 #10 $7 m = 5 #10-4 m ( ) = 0.0025 m = 2.5 mm
! Similarly, interference can occur when light waves are reflected from the top and bottom surfaces of a soap film or oil slick.! The difference in the path length of the two waves can produce an interference pattern.! This is called thin-film interference.
! Different wavelengths of light interfere constructively or 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 interference pattern 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 to interference of light coming from different parts 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 is 0.4 mm wide. The diffraction pattern produced is observed on a 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?!= 550 nm = 5.5 x 10-7 m w = 0.4 mm = 4 x 10-4 m x = 3.0 m y = "x w ( ) 3.0 m ( ) 5.5 #10 $7 m = 0.4 #10-3 m ( ) = 0.0041 m = 4.1 mm
How wide is the central bright fringe of this diffraction pattern? The central bright fringe extends out to the first dark fringe on either side, so its width is just twice the distance y:!= 550 nm = 5.5 x 10-7 m w = 0.4 mm = 4 x 10-4 m x = 3.0 m 2y = 2( 4.1 mm) = 8.2 mm
! The diffraction pattern produced by a square opening has an array of bright spots.! Looking at a star or distant street light through a window screen can produce a similar diffraction pattern.
! A diffraction grating has a very large number of slits very closely spaced.! Whenever the path difference is equal to an integer multiple of the light wavelength, we get a strong bright fringe for that wavelength.! Different wavelengths will appear at different points on the screen, spreading the light into its spectrum. d y x = m", m = 0,±1,±2,...! Diffraction gratings in spectrometers are used to separate and measure the wavelengths of light.! Gratings also produce the effects seen in novelty glasses, reflective gift wrappings, and in the colors seen on a CD.
Polarized Light $ How do polarizing sunglasses and camera filters 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 the vertical plane, and the magnetic field is horizontal.! Actually, the electric field could oscillate in the horizontal with the magnetic field in the vertical plane, or the electric field could oscillate at some angle to the horizontal.! As long as the electric field is always pointing in the same direction for all the waves, the light is polarized.
! The electric field vector oscillates in a single direction for polarized light.! Unpolarized light has random directions of orientation. #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 component of each electric field vector that is aligned with the filter s axis of transmission to pass through. #The component perpendicular to this axis is absorbed.
! Reflection from a smooth surface of a transparent material such as glass or water can also polarize light. #Incoming sunlight is unpolarized. #When the angle between the reflected wave and the transmitted wave is a right angle, the reflected wave is polarized. #Polarizing sunglasses can help reduce glare from reflected sunlight.
! Many interesting and colorful effects are related to the phenomenon of birefringence. " Birefringence is also called double refraction. " Light with different polarizations travels with different velocities when passing through a birefringent material. " This causes colorful displays when the birefringent material is viewed through crossed polarizers. #Calcite crystals are a good example of birefringent material. #Lines are doubled when viewed through a calcite crystal.
! Many interesting and colorful effects are related to the phenomenon of birefringence. " Birefringence is also called double refraction. " Light with different polarizations travels with different velocities when passing through a birefringent material. " This causes colorful displays when the birefringent material is viewed through crossed polarizers. #A plastic lens under compression shows stress birefringence when viewed between crossed polarizers.