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Introductory Electromagnetism Problems Laboratory
DVD
Goals: Use physics knowledge to check media descriptions for consistency. Apply rules for interference and diffraction to a physical device.
PROBLEM The digital video disk (DVD) is a standard medium for storing information such as movies, music, or software. The DVD is made from multiple layers of polycarbonate plastic which includes one or more layers with encoded information. The encoded infor- mation is read using the diffraction of light. The diffraction from a DVD can be seen when it is held under light and a spectrum of colors appears. (Photo engagetHD.com)
The DVD is a widespread technology and is well documented on the internet. In this lab you will check the facts from one internet site to see how well the description of a DVD matches the physics of the device.
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PROBLEM SKILLS When coherent light from a laser is reflected off two surfaces at different distances it can the light can be subject to either constructive or destructive interference. If a surface is at a distance to reflect a wavelength λ with constructive intereference then the light will have destructive intereference when twice the difference in distance d is equal to a phase shift of 180o^. This can be expressed mathematically as
(EQ 1)
where m is an integer.
Interference need not be completely constructive or destructive. For an arbitrary wave- length shift L , the phase difference Δφ in radians is
(EQ 2)
The length of a spiral depends on its inner radius R 1 , outer radius R 2 and the change in radius Δ r with each turn of the spiral. If the average circumference of one turn of a spi- ral is 2π( R 1 + R 2 )/2 and the number of turns is ( R 2 - R 1 )/Δ r , then the length S is approxi- mately
(EQ 3)
is the difference inchanged When The extra patit can In the real world there are multi- ple sources of fields superposed on each other. These fields can be considered back- ground noise to the signal field from the earth. One technique to estimate the effect of noise sources is to consider a worst case scenario. If the field from the background source is greater that 1/10 of the signal then it might be something to worry about for measurements with no more than one significant figure of accuracy.
A current in a wire produces a magnetic field ( B ) measured in tesla. If the current ( I ) in a long straight wire is measured in amps, the field at a distance ( r ) in meters is:
BACKGROUND INFORMATION
The web site HowStuffWorks.com has a detailed description of DVD technology. The technology consists of two parts: the player and the disk. The following facts are con- densed from that web site.
The DVD player has three parts. There is a variable speed motor that spins the disk at 200 to 500 rpm. There is a laser with a wavelength of 640 nm that reflects of the mir- rored surface of the DVD and is measured by an optical pickup that can tell the differ- ence in reflectivity between the flat surface of the disk an small bumps on it. Finally there is a tracking motor that positions the laser at a particular radius from the center of the disk and slows the DVD down from 500 rpm when it is tracking the innermost part of the data down to 350 rpm at the outermost part of the disk.
2 d m^1 2 = ⎝⎛ +---⎠⎞^ λ
Δφ L λ =⎝⎛ ---^ – m ⎠⎞^2 π
S 2 π
R 1 + R 2 2 ⎝⎛ ------------------⎠⎞^
R 2 – R 1 Δ r ⎝⎛ ------------------⎠⎞^
π ( R 22 – R 12 ) Δ r = =^ --------------------------
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OBSERVATIONS For each observation below write a short paragraph to explain your thinking.
The picture shows a whole spectrum of color, yet the DVD is designed for one fre- quency of laser light. What is causing a spectrum of color in the picture?
Could rounding errors or significant figures account for any discrepancies in the data given by the web site if complete destructive interference is assumed?
How consistent were the different groups analyses of the web site’s values to give destructive interference? Is this a good way to check a source for consistency with physics?
How well did your group’s first estimate of inner radius in step 8 match with the recal- culated value in step 12?
Is your length to hold the data in step 14 consistent with either of the lengths of the spi- ral compared in step 10?
Could more data be placed in a single spiral on one DVD?
