SPH4U UNIVERSITY PHYSICS THE WAVE NATURE OF LIGHT L (P.477-484) Particle Theory vs. Wave Theory At the en of the 1600s an into the 1700s, the ebate over the nature of light was in full swing. Newton s theory of light particles face challenges from leaing scientists such as Christiaan Huygens. Huygens writings on the wave theory of light propose that light travelle in waves through an omnipresent ether, like soun travelling through air. December 8, 2012 4U4 - Young's Double-Slit Experiment 1 Interference During this time, many researchers focuse on the question of interference. If light behaves like a wave, a similar experiment using two light sources shoul reveal bright areas (constructive interference) an ark areas (estructive interference) on a screen. However, researchers coul not etect it. December 8, 2012 4U4 - Young's Double-Slit Experiment 2 1
Interference We now know that the experiments faile for two simple but very important reasons. Î Atoms sen out a burst of light energy about every 10-8 s so the probability that the atoms in each source woul emit their light waves in phase is nearly zero the result is an interference pattern that changes in an irregular fashion an is impossible to see. Ï Compare to the wavelength of light, the istance between the sources was much too large the result is light an ark areas on the screen that are too close together to be observe. December 8, 2012 4U4 - Young's Double-Slit Experiment 3 Interference These conitions were exceeingly ifficult for scientists to create in the 1700s. In aition, since physicists i not even know whether light behave like a particle or a wave, they ha no way of knowing what the wavelength might be. It took nearly 100 years after Newton an Huygens presente their theories of light for the ebate to be resolve. December 8, 2012 4U4 - Young's Double-Slit Experiment 4 At the en of the 1700s, Thomas Young evise an ingenious experiment that prouce an interference pattern with light. Using one monochromatic light source, Young allowe the light to fall onto an opaque material with a single, narrow slit. December 8, 2012 4U4 - Young's Double-Slit Experiment 5 2
Accoring to Huygens principle, this slit acte as a new source. The light passing through the single slit sprea as it travelle to a secon opaque barrier that ha two narrow slits place very close together. As a result, the light leaving the ouble slits was essentially coherent. December 8, 2012 4U4 - Young's Double-Slit Experiment 6 The light that passe through the ouble-slit barrier fell on a nearby screen, proucing the historic pattern of light an ark lines cause by the interference of light waves. Young s results catapulte the wave moel for light into centre stage, where it woul remain unchallenge for more than 100 years. December 8, 2012 4U4 - Young's Double-Slit Experiment 7 Young experimente with this set-up for more than two years before he realize that the ouble slits ha to be so close together that they almost appeare to be one slit to the unaie eye. December 8, 2012 4U4 - Young's Double-Slit Experiment 8 3
Young was successful where others ha faile for several reasons. Î He use a monochromatic (single wavelength) light source. Ï The ouble slits acte as two sources an were space much more closely together than possible if two separate light sources were use. Ð The light passing through the initial single slit acte as a point source. When a wave front from the point source reache the ouble slits, two parts of the same wave front became new sources for the ouble slits an were therefore coherent. December 8, 2012 4U4 - Young's Double-Slit Experiment 9 YOUNG S DOUBLE-SLIT EXPERIMENT early attempts to show the interference of light were unsuccessful b/c: the sources were not coherent, an the sources were too far apart December 8, 2012 4U4 - Young's Double-Slit Experiment 10 YOUNG S DOUBLE-SLIT EXPERIMENT (continue...) Young was successful for three main reasons: Î he use a monochromatic (i.e. single wavelength) light source Ï the ouble slits were very close together Ð the ouble slits acte as two point sources that were coherent (i.e. in phase) December 8, 2012 4U4 - Young's Double-Slit Experiment 11 4
YOUNG S DOUBLE-SLIT EXPERIMENT (continue...) prouce a series of light an ark fringes on a screen place in the path of the light pattern resemble the results of the interference of water waves in a ripple tank was evience for the wave nature of light December 8, 2012 4U4 - Young's Double-Slit Experiment 12 The bright an ark fringes are alternate regions of constructive an estructive interference, respectively. To analyze the interference, you nee to etermine the path length ifference between each slit an the screen. December 8, 2012 4U4 - Young's Double-Slit Experiment 13 To simplify the analysis, we assume that: 1. the screen is a long way from the slits an so L >> 2. since L >>, the path lengths L 1 an L 2 are nearly parallel 3. since L 1 an L 2 are nearly parallel, the angles of the path lengths L 1 an L 2 from each of the slits to the point P on the screen are approximately equal 4. the wavelength 8 is much smaller than December 8, 2012 4U4 - Young's Double-Slit Experiment 14 5
Since the slits are separate by a istance, the path length ifference between L 2 an L 1 is given by: L = sinθ December 8, 2012 4U4 - Young's Double-Slit Experiment 15 For the two waves to be in phase when they reach the screen, an thus for constructive interference to occur, this path length ifference nees to be a whole number of wavelengths. sinθ m = m λ m = 0, 1, 2,... The light fringes, or maxima, are calle zeroorer maximum, first-orer maximum, an so on for m = 0, 1, 2,... In this notation, m = 0 enotes the maximum in the centre of the screen. December 8, 2012 4U4 - Young's Double-Slit Experiment 16 Similarly, for the two waves to be out of phase when they reach the screen, an thus for estructive interference to occur, the path length ifference nees to be (n-1/2)8. 1 ( n - ) sinθn = 2 λ n = 1, 2,... The ark fringes, or minima, are calle firstorer minimum, secon-orer minimum, an so on for n = 1, 2,... December 8, 2012 4U4 - Young's Double-Slit Experiment 17 6
YOUNG S DOUBLE-SLIT EXPERIMENT (continue...) m λ sinθ m = 1 ( n- ) 2 λ sinθn = where m = 0, 1, 2, (for bright fringes) n = 1, 2,... (for ark fringes) is the slit separation (m) 2 is the location of the m th maxima/n th minima 8 is the wavelength of the light (m) December 8, 2012 4U4 - Young's Double-Slit Experiment 18 1. The thir-orer ark fringe of 660 nm light is observe at an angle of 20.0E when the light falls on two narrow slits. Determine the slit separation. = 4.8 x 10-6 m December 8, 2012 4U4 - Young's Double-Slit Experiment 19 In aition, the equation to etermine the istance of each bright fringe from the centre of the screen (m = 0) is: m L λ x m = December 8, 2012 4U4 - Young's Double-Slit Experiment 20 7
Similarly, the equation to etermine the istance of each ark fringe from the centre of the screen is: ( n - ) 2 x = 1 n L λ December 8, 2012 4U4 - Young's Double-Slit Experiment 21 Although L actually has ifferent values for each maxima/minima, L is so large compare to an the values of L for the various noal an anti-noal lines are so similar, that we can treat L as a constant, being essentially equal to the perpenicular istance from the slits to the screen. December 8, 2012 4U4 - Young's Double-Slit Experiment 22 YOUNG S DOUBLE-SLIT EXPERIMENT (continue...) m L λ x m = ( n - ) 2 x = 1 n L λ where m = 0, 1, 2, (for bright fringes) n = 1, 2,... (for ark fringes) is the slit separation (m) 8 is the wavelength of the light (m) L is the perpenicular istance to the screen (m) x is the istance of the m th maxima/n th minima from the centre of the screen (m) December 8, 2012 4U4 - Young's Double-Slit Experiment 23 8
2. Two slits are separate by 0.20 mm an prouce an interference pattern. The fifth maximum is 12.8 cm from the central maximum. The wavelength of the light use is 550 nm. Determine the istance at which the screen is place. L = 9.3 m December 8, 2012 4U4 - Young's Double-Slit Experiment 24 In either case, the separation between any two ajacent fringes is: L λ x = which can then be rearrange to etermine the approximate wavelength of light: λ = x L December 8, 2012 4U4 - Young's Double-Slit Experiment 25 YOUNG S DOUBLE-SLIT EXPERIMENT (continue...) x λ = L where 8 is the approximate wavelength of light (m) is the separation of the slits (m) )x is the separation between ajacent fringes (m) L is the perpenicular istance to the screen (m) This relationship applies equally to ajacent ark/bright fringes. The relationship is only goo for very small angles. December 8, 2012 4U4 - Young's Double-Slit Experiment 26 9
3. A ouble-slit experiment is carrie out with slit spacing = 0.41 mm. The screen is at a istance of 1.5 m. The bright fringes at the centre of the screen are separate by a istance )x = 1.5 mm. (a) Determine the wavelength of the light. (a) 8 = 4.1 x 10-7 m December 8, 2012 4U4 - Young's Double-Slit Experiment 27 3. A ouble-slit experiment is carrie out with slit spacing = 0.41 mm. The screen is at a istance of 1.5 m. The bright fringes at the centre of the screen are separate by a istance )x = 1.5 mm. (b) Determine the spacing of the bright fringes when a source with a wavelength 600 nm is use. (b) )x = 2.2 x 10-3 m December 8, 2012 4U4 - Young's Double-Slit Experiment 28 4. In an interference experiment, re light (600 nm) passes through a ouble slit. On a screen 1.5 m away, the istance between the 1 st an 11 th ark bans is 13.2 cm. (a) What is the spacing between ajacent noal lines? (a) )x = 1.32 cm (11 lines = 10 )x) December 8, 2012 4U4 - Young's Double-Slit Experiment 29 10
4. In an interference experiment, re light (600 nm) passes through a ouble slit. On a screen 1.5 m away, the istance between the 1 st an 11 th ark bans is 13.2 cm. (b) What is the separation of the slits? (b) = 6.8 x 10-5 m December 8, 2012 4U4 - Young's Double-Slit Experiment 30 4. In an interference experiment, re light (600 nm) passes through a ouble slit. On a screen 1.5 m away, the istance between the 1 st an 11 th ark bans is 13.2 cm. (c) What woul the spacing be, between ajacent noal lines, if blue light (450 nm) were use? (c) )x = 9.9 x 10-3 m December 8, 2012 4U4 - Young's Double-Slit Experiment 31 More Developments in the Theory of Light Young s evience for the wave nature of light was not accepte by the scientific community until 1818, when Augustin Fresnel propose his own wave theory, complete with the mathematics. A mathematician name Simon Poisson showe how Fresnel s equations preicte a unique pattern when light is projecte past a small soli object, as shown below. December 8, 2012 4U4 - Young's Double-Slit Experiment 32 11
More Developments in the Theory of Light Poisson s argument was that, if light behave as a wave, then the light iffracting aroun the eges of the isc shoul interfere constructively to prouce a bright spot at the centre of the iffraction pattern. This was impossible accoring to the particle theory of light. December 8, 2012 4U4 - Young's Double-Slit Experiment 33 More Developments in the Theory of Light In 1818, Poisson s preiction was teste experimentally by Dominique Arago, an, to many people's surprise, he successfully observe the bright spot, which is now known as Poisson s bright spot. The experiment also verifie the wave theory of light. December 8, 2012 4U4 - Young's Double-Slit Experiment 34 More Developments in the Theory of Light WAVE THEORY OF LIGHT Young s evience for the wave nature of light was not accepte until 1850 Poisson s bright spot provie the experimental evience POISSON S BRIGHT SPOT light iffracting aroun the eges of a isc prouces a bright spot at the centre of the interference pattern December 8, 2012 4U4 - Young's Double-Slit Experiment 35 12
More Developments in the Theory of Light By 1850 the valiity of the wave theory of light ha been generally accepte. For some time afterwar, the mathematical consequences of the wave theory were applie to numerous aspects of the properties of light. But the wave theory was not aequate to explain the movement of light through the vacuum of space, since waves require a material meium for their transmission. The power of the wave theory was now so great, however, that scientists theorize a flui filling all space, from the space between atoms to the space between planets. They calle it ether. Many experiments were attempte to etect this ether, but none was successful. December 8, 2012 4U4 - Young's Double-Slit Experiment 36 5. So, is light a wave or a particle? It has become obvious that light is not just a wave an not just a particle. It is both. It has a ual nature, a property referre to by physicists as wave-particle uality. We reach this conclusion because both theories of light have been shown to have valiity, base on very strong experimental evience. It is clear that light is a much more complex phenomenon than just a beam of particles or just a simple wave. December 8, 2012 4U4 - Young's Double-Slit Experiment 37 U Check Your Learning TEXTBOOK P.482 Q.1-3 P.484 Q.1,2,5 December 8, 2012 4U4 - Young's Double-Slit Experiment 38 13