Diffraction and Interference of Light By: Karen Cooper

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

Interference is… the process in which two or more light, sound, or electromagnetic 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.

19.1 When Light Waves Interfere

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 (1629-1695) 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.

http://demonstrations.wolfram.com/HuygenssPrinciple/ (picture on 444, 19-1) Karen Cooper

English physician Thomas Young (1773-1829) read Newton's book on optics: convinced Newton's description of light behavior in optics could be explained if light were a wave with an extremely small wavelength.

Vocabulary Interference fringes(19.1): pattern of dark/light bands on a screen due to constructive/destructive interference of light waves passing through two narrow, closely spaced slits Monochromatic light (19.1): light of only one wavelength Coherent waves(19.1): waves that are in phase--crests and troughs reach the same point together

Young’s two-slit experiment

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.

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.

(picture on 445 - 19-2) Cheng, Poon S., Mrs. "Chapter 4: Young’s Double Slit Experiment." Singapore A Level Physics Syllabus. N.p., n.d. Web. 6 Feb. 2011.<http://h2physics.org/>.

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

Diffraction of white light

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.

Blue Light White Light Red Light (picture on page 445 - 19-3) (19-3 c) Karen Cooper White Light. N.d. Multiple-beam interference. N.p., 2009. Web. 7 Feb.2011. <http://www.itp.uniannover.de/~zawischa/ITP/multibeam.html>. Red Light. N.d. Multiple-beam interference. N.p., 2009. Web. 7 Feb.2011. <http://www.itp.uniannover.de/~zawischa/ITP/multibeam.html>.

Measuring the Wavelength of a Light Wave

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.

(diagram on page 447 - 19-4) Karen Cooper

Equation: Wavelength Using Double Slit Interference Distance between P0 and P1: x Distance between screen and slits: L Separation of two slits: d Equation: x/L = λ/d Wavelength 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. EX: walking near the band room, you can hear the band before you actually see them. Playing Piano. N.d. Piano Tutorial. N.p., 2010. Web. 8 Feb. 2011., http://www.pianotutorial.com/articles/piano-in-a-band.html>.

From one to many slits

Light passes through a single slit's small opening Light passes through a single slit's small opening. This creates a central band with dimmer bands on either side. (figure on page 449 - 19-5) Red Light. N.d. Multiple-beam interference. N.p., 2009. Web. 7 Feb.2011. <http://www.itp.uniannover.de/~zawischa/ITP/multibeam.html>.

A single slit had a width called w 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. Any slit in the top half will have another slit in the bottom with a distance of w/2.

(figure on page 449 - 19-6) Karen Cooper

Measuring a wavelength of light

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. Paths differ by λ/2 and separation between slits is w/2 instead.

Red Light. N. d. Multiple-beam interference. N. p. , 2009. Web. 7 Feb (figure on page 450 - 19-7) Karen Cooper White Light. N.d. Multiple-beam interference. N.p., 2009. Web. 7 Feb.2011. <http://www.itp.uniannover.de/~zawischa/ITP/multibeam.html>.

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

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

19.2 Applications of Diffraction

The colors seen on a beetles back are caused by diffraction The colors seen on a beetles back are caused by diffraction. Hard ridges cover the beetles back and the spaces between them cause diffraction like slits do. This produces interference effects. The ridges and slits enhance the interference pattern in series. A CD does the same thing, diffracting light between its grooves. Susan. Lavender Beetle. N.d. ShopCurious. Syrox eMedia, 31 July 2009. Web. 7 Feb. 2011. http://shopcurious.blogspot.com/2009/07/curious- colours-of-nature-in-fashion.html>.

Diffraction Gratings

Diffraction gratings are used to measure the wavelength of light 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.

Picture of jewelry or CD creating spectrum. Diamond. N.d. Colour Museum. N.p., 2009. Web. 7 Feb. 2011. <http://www.coloure.experience.org/index.htm>. Picture of jewelry or CD creating spectrum. CD. N.d. Multiple-beam interference. N.p., 2009. Web. 7 Feb. 2011. <http://www.itp.uniannover.de/~zawischa/I TP/multibeam.html>.

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 θ Distance between P0 and P1: x Distance between screen and slits: L Separation of two slits: d Wavelength: λ

A grating spectroscope is used to measure light wavelengths A grating spectroscope is used to measure light wavelengths. As you look through, a light falls on the slit and creates a series of bright bands on either side of a central band. At the calibrated base of the spectrometer, the angle θ is shown. Since d is known, λ can be calculated.

(figure on page 454-455 19- 9, 10) Ng., H. K., Dr. Diffraction Grating Spectrometer. N.d. N.p., 30 Dec. 1996. Web. 8 Feb. 2011.<http://www.physics.fsu.edu/users/ng/courses/phy2054c/ labs/expt09/expt-09.htm>.

Vocabulary Diffraction grating(19.2): a device with parallel ridges that reflect light and form an interference pattern.

Resolving Power of Lenses

A telescopes lens diffracts light just as a slit does 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. Rayleigh-Criteria: Stars. N.d. Wikimedia Commons. N.p., 30 May 2010. Web. 8 Feb. 2011. <http://commons.wikimedia.org/wiki/File:Rayleigh_fromcalculateddiffractiondisc_edit edwithgimp.png>.

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 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.

Vocabulary Rayleigh criterion(19.2): when the central bright band of one star falls on the first dark band of the second, the two stars will be just resolved.

Works Cited Zitzewitz, Paul W. Physics Principles and Problems. 2002 ed. New York: Glencoe, 2002. Print. Tipler, Paul A. Physics for Scientists and Engineers. 4th Ed. New York: W.H. Freeman and Company, 1999. Cheng, Poon S., Mrs. "Chapter 4: Young’s Double Slit Experiment." Singapore A Level Physics Syllabus. N.p., n.d. Web. 6 Feb. 2011.<http://h2physics.org/>. Susan. Lavender Beetle. N.d. ShopCurious. Syrox eMedia, 31 July 2009. Web. 7 Feb. 2011. http: //shopcurious.blogspot.com/2009/07/curious- colours-of-nature-in-fashion.html>. Diamond. N.d. Colour Museum. N.p., 2009. Web. 7 Feb. 2011. <http://www.coloure.experience.org/ index.htm>. White Light. N.d. Multiple-beam interference. N.p., 2009. Web. 7 Feb.2011. <http://www.itp. uniannover.de/~zawischa/ITP/multibeam.html>. CD. N.d. Multiple-beam interference. N.p., 2009. Web. 7 Feb. 2011.<http://www.itp.uniannover .de/~zawischa/ITP/multibeam.html>. Playing Piano. N.d. Piano Tutorial. N.p., 2010. Web. 8 Feb. 2011. ,http://www.pianotutorial.com/articles /piano-in-a-band.html>. Rayleigh-Criteria: Stars. N.d. Wikimedia Commons. N.p., 30 May 2010. Web. 8 Feb. 2011. <http://commons .wikimedia.org/wiki/File:Rayleigh_fromcalculated diffractiondisc_editedwithgimp.png>. Ng., H. K., Dr. Diffraction Grating Spectrometer. N.d. N.p., 30 Dec. 1996. Web. 8 Feb. 2011.<http:// www.physics.fsu.edu/users/ng/courses/phy2054c /labs/expt09/expt-09.htm>. Constructive Interference. Tipler, Paul A. Physics for Scientists and Engineers. 4th Ed. New York: W.H. Freeman and Company, 1999. Destructive Interference. Tipler, Paul A. Physics for Scientists and Engineers. 4th Ed. New York: W.H. Freeman and Company, 1999.