Chapter 19 Interference and DiffractionInterference and Diffraction

Diffraction is… the bending of waves, esp. sound and light waves, around obstacles in their path.the bending of waves, esp. sound and light waves, around obstacles in their path.

Interference is… electromagnetic waves of the same frequency combine to reinforce or cancel each otherelectromagnetic waves of the same frequency combine to reinforce or cancel each other the amplitude of the resulting wave being equal to the sum of the amplitudes of the combining waves the amplitude of the resulting wave being equal to the sum of the amplitudes of the combining waves

Isaac Newton believed light was made up of fast moving, tiny particles- he called these corpuscles. He thought the edges of shadows weren't perfectly sharp because of infraction. Newton probably never thought that the light's wavelengths might be so tiny that they could produce such small effects of diffraction.Isaac Newton believed light was made up of fast moving, tiny particles- he called these corpuscles. He thought the edges of shadows weren't perfectly sharp because of infraction. Newton probably never thought that the light's wavelengths might be so tiny that they could produce such small effects of diffraction.

Diffraction

The Dutch scientist Christian Huygens ( ) proposed a wave model to explain diffraction. These wavelets expand in every direction and are in step with one another. Light sources consist of an infinite number of points, which generate a plane wave front.The Dutch scientist Christian Huygens ( ) proposed a wave model to explain diffraction. These wavelets expand in every direction and are in step with one another. Light sources consist of an infinite number of points, which generate a plane wave front.

Karen Cooper

Young could measure light's wavelengths and provided additional evidence of the waves nature of light. By directing the beam of light at two narrow, closely spaced slits in barrier, light diffracted and the two rays overlapped. This created light and dark bands.Young could measure light's wavelengths and provided additional evidence of the waves nature of light. By directing the beam of light at two narrow, closely spaced slits in barrier, light diffracted and the two rays overlapped. This created light and dark bands. Young’s two-slit experiment

Only a small part of light passes through a single slit, emitting one wavelength. The waves are in a phase, crests reaching the same point at same time, so did troughs.Only a small part of light passes through a single slit, emitting one wavelength. The waves are in a phase, crests reaching the same point at same time, so did troughs. Waves spread after passing through slit and fall on a double slit. Waves diffracted from double slit act as two sources of new circular waves spreading out from barrier.Waves spread after passing through slit and fall on a double slit. Waves diffracted from double slit act as two sources of new circular waves spreading out from barrier.

Cheng, Poon S., Mrs. "Chapter 4: Young’s Double Slit Experiment." Singapore A Level Physics Syllabus. N.p., n.d. Web. 6 Feb

Where two crests overlap (waves interfere constructively), light intensity increases creating a bright band on screen. Crests and troughs meet (interfere destructively) and cancel one another to create dark region.Where two crests overlap (waves interfere constructively), light intensity increases creating a bright band on screen. Crests and troughs meet (interfere destructively) and cancel one another to create dark region.

Constructive interference produces a bright central band and other bands on either side. Dark areas are where destructive interference occurs between bright bands.Constructive interference produces a bright central band and other bands on either side. Dark areas are where destructive interference occurs between bright bands. White light in double slit diffraction causes colors instead of light/dark bands. Positions of constructive/destructive bands depends on light's wavelength.White light in double slit diffraction causes colors instead of light/dark bands. Positions of constructive/destructive bands depends on light's wavelength. Diffraction of white light

Constructive : positive growth. Destructive : negative growth. Constructive Interference. Tipler, Paul A. Physics for Scientists and Engineers. 4th Ed. New York: W.H. Freeman and Company, Destructive Interference. Tipler, Paul A. Physics for Scientists and Engineers. 4th Ed. New York: W.H. Freeman and Company, 1999.

Red Light Blue Light White Light White Light. N.d. Multiple-beam interference. N.p., Web. 7 Feb Red Light. N.d. Multiple-beam interference. N.p., Web. 7 Feb Karen Cooper

No matter the wavelength used, light reaching the point Po travels the same distance from the slits. Wavelengths interact constructively. The first bright band on either side of the central band are called first- order line.No matter the wavelength used, light reaching the point Po travels the same distance from the slits. Wavelengths interact constructively. The first bright band on either side of the central band are called first- order line. Measuring the Wavelength of a Light Wave

Karen Cooper

Equation: Wavelength Using Double Slit Interference Distance between P0 and P1: xDistance between P0 and P1: x Distance between screen and slits: LDistance between screen and slits: L Separation of two slits: dSeparation of two slits: d Equation: x/L = λ/dEquation: x/L = λ/d Wavelength Using Double-Slit Interference: λ = xd/LWavelength Using Double-Slit Interference: λ = xd/L

Single-Slit Diffraction

Grimaldi first noted that diffraction occurs in both light and sound, but since light's wavelengths are much smaller, diffraction is less obvious.Grimaldi first noted that diffraction occurs in both light and sound, but since light's wavelengths are much smaller, diffraction is less obvious. EX: walking near the band room, you can hear the band before you actually see them.EX: walking near the band room, you can hear the band before you actually see them. Playing Piano. N.d. Piano Tutorial. N.p., Web. 8 Feb ,

Light passes through a single slit's small opening. This creates a central band with dimmer bands on either side.Light passes through a single slit's small opening. This creates a central band with dimmer bands on either side. Red Light. N.d. Multiple-beam interference. N.p., Web. 7 Feb From one to many slits

A single slit had a width called w. Imagine the slit is divided into large number of smaller slits called dw.A single slit had a width called w. Imagine the slit is divided into large number of smaller slits called dw. Choosing a pair of slits so each has the same separation: divide the slit into two equal parts, pairs are separated by distance of w/2.Choosing a pair of slits so each has the same separation: divide the slit into two equal parts, pairs are separated by distance of w/2. Any slit in the top half will have another slit in the bottom with a distance of w/2.Any slit in the top half will have another slit in the bottom with a distance of w/2.

Karen Cooper

Measuring a wavelength of light

The slit is illuminated, so a central bright band appears at Po on screen.The slit is illuminated, so a central bright band appears at Po on screen. The dark band from the central light band create a situation similar to the double-slit interference.The dark band from the central light band create a situation similar to the double-slit interference. Paths differ by λ/2 and separation between slits is w/2 instead.Paths differ by λ/2 and separation between slits is w/2 instead.

White Light. N.d. Multiple-beam interference. N.p., Web. 7 Feb Red Light. N.d. Multiple-beam interference. N.p., Web. 7 Feb Karen Cooper

Equation: Ratio of Sides of a Triangle x/L = (λ/2)/(w/2) = λ/wx/L = (λ/2)/(w/2) = λ/w Distance between slits and screen: LDistance between slits and screen: L Distance between Po and P1: xDistance between Po and P1: x Wavelength: λWavelength: λ Width of a single slit: wWidth of a single slit: w

Equation: Distance Between Central and 1 st Dark Bands x = λL/wx = λL/w Distance between slits and screen: LDistance between slits and screen: L Distance between Po and P1: xDistance between Po and P1: x Wavelength: λWavelength: λ Width of a single slit: wWidth of a single slit: w

Diffraction Gratings

Diffraction gratings are used to measure the wavelength of light. Diffraction gratings are made by scratching very fine lines on glass using the point of a diamond. The spaces between the scratches are like slits.Diffraction gratings are used to measure the wavelength of light. Diffraction gratings are made by scratching very fine lines on glass using the point of a diamond. The spaces between the scratches are like slits. EX: jewelry creates spectrum like that on the surface of a CD.EX: jewelry creates spectrum like that on the surface of a CD.

CD. N.d. Multiple-beam interference. N.p., Web. 7 Feb Diamond. N.d. Colour Museum. N.p., Web. 7 Feb

The interference pattern produced by diffraction grating has bright bands cause by a double-slit. Individual colors can be distinguished more easily with this and wavelengths can be measured more precisely in diffraction grating then double-slits.The interference pattern produced by diffraction grating has bright bands cause by a double-slit. Individual colors can be distinguished more easily with this and wavelengths can be measured more precisely in diffraction grating then double-slits.

Equation: Wavelength Using a Diffraction Grating λ = xd/L = d sin θλ = xd/L = d sin θ Distance between P0 and P1: xDistance between P0 and P1: x Distance between screen and slits: LDistance between screen and slits: L Separation of two slits: dSeparation of two slits: d Wavelength: λWavelength: λ Phase separation: θPhase separation: θ

Ng., H. K., Dr. Diffraction Grating Spectrometer. N.d. N.p., 30 Dec Web. 8 Feb

Resolving Power of Lenses

A telescopes lens diffracts light just as a slit does. The pattern is wide if the lens is small.A telescopes lens diffracts light just as a slit does. The pattern is wide if the lens is small. EX: a single star will appear spread out while two close stars may blur together so it's unknown if there are two or only one.EX: a single star will appear spread out while two close stars may blur together so it's unknown if there are two or only one. Rayleigh-Criteria: Stars. N.d. Wikimedia Commons. N.p., 30 May Web. 8 Feb

Lord Rayleigh established that when the central bright band of one star falls on the first dark band of the second, the two stars will be resolved. By reducing the lens's size, the effects of diffraction can be reduced.Lord Rayleigh established that when the central bright band of one star falls on the first dark band of the second, the two stars will be resolved. By reducing the lens's size, the effects of diffraction can be reduced.

The resolving power of microscopes is limited by diffraction as well. The lens can't be enlarged, but the wavelength of light can be reduced.The resolving power of microscopes is limited by diffraction as well. The lens can't be enlarged, but the wavelength of light can be reduced. Since blue light forms a narrower pattern than red light, it is used for microscopes while red light is used for telescopes.Since blue light forms a narrower pattern than red light, it is used for microscopes while red light is used for telescopes.