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Physics S-1ab Lab 10: Wave Optics Summer 2007

Introduction

Preparation: Before coming to lab, read the lab handout and all course requiredreading in Giancoli through Chapter 25. Be sure to bring to lab: this handout writingpaper, a ruler, a calculator and your copy of the Lab Companion.

Post Lab Questions: At the beginning of your lab section, you will be given anadditional handout with a series of questions to be answered and handed in at the endof the experiment. Try to answer these questions with one or two concise sentences.

Experiment Overview In Part I you use a machinist rule and a laser to investigatethe interference of light scattered from a periodic set of stripes and from this,determine the wavelength of the light. In Part II you will use the laser to make

quantitative measurements of light scattered from the surface of a CD to learn aboutthe microscopic structure of its recorded information.

Part I: Measuring the Wavelength of Light

What happened to the law of reflection?

In this experiment you will use a steel ruler to measure the wavelength of light emitted by alaser. The laser produces a narrow intense beam of monochromatic (i.e., single wavelength)light. The ruler has a shiny, metallic finish. Consequently, if you reflect the laser light off thesurface of the ruler, it behaves like a mirror with the angle of reflection equal to the angle ofincidence. However, if you shine the laser beam onto the part of the ruler where the blackdivision marks are (see Fig. 2), a surprising thing happens: not only does the light reflect atthe expected angle, but one observes that there are many additional reflections. One mightwonder why the law of reflection suddenly seems to be violated just because there are somenon-reflective marks on the ruler.

One way to think about this is to use Huygens wavelet picture in which all reflections arepossible. Every point of the ruler bathed by the incoming laser light will be the source of newwavelets radiating out in all directions. In most cases, there is cancellation, destructive

interference, for these paths, except for those paths that do not deviate much (less than from the straight (and minimum length) path (for which the reflected angle equals theincident angle). However, the non-reflective division marks on the ruler eliminate some ofthe possible wavelets, thereby preventing this wholesale cancellation of paths.


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In other words, the additional bright spots one sees on the wall are due to reflections that areonly possible because we are preventing them from being canceled by destructiveinterference. We secure morereflections by arranging for fewer possibilities of reflection!!Continuing with this line of reasoning thus suggests that the bright spots are due toconstructive interference.

Figure 1, which is not to scale, shows the experimental arrangement. The ruler is placed on atable about 2 m (distance L) from the wall, and the laser is positioned so that the beam just

strikes near the end of the ruler at a grazing angle 0 (Note that 0 is complementary to the

angle to the normal, 0 ). Part of the laser beam misses the ruler completely and continues

undeviated to the wall (direct beam). Many reflections will appear on the wall, but, to keepthe drawing simple, only two are shown in the figure. The brightest reflected spot, the central

bright spot, corresponds to the reflection whose angle is equal to the angle, 0 . Many more

reflection spots will be present, above and below 0 .

You may recall that the bright spots from a diffraction grating occur at angles such that

sin / n n d = (1)

but this equation describes light arriving perpendicular to the surface ( 0 0 = ). In this lab you

have light arriving at an angle to the normal 0 0 , and for this more general case,

constructive interference (bright spots) occur according to

0y 1y

L

laserruler

central reflectedbright spot

first spot abovecenter

wall

direct beam

1

0 0tan / y L = and 1 1tan / y L =

Figure 1

0 0

0

0


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Measurement procedure

(a)

Allow the ruler to slightly overhang the edge of the table then adjust the angle ofthe laser beam. The grazing angle should be < 2, and the ruler must beperpendicular to the wall. Tape a piece of paper on the wall for viewing andmarking the positions of the various spots.

Note : The laser can be kept turned on using a clothes pin, but please turn off the laser

when not performing measurements !

Notice that on your ruler there are a series of marks with different spacings and lengthsinterspersed.

Make sure you are using onlythe 1/64 marks.

(b)

Verify which set of marks are producing the spots you see on the wall by slidingthe ruler to the left and right and see sets of spots appear and disappear.

(c)Record as many spots as you can. The angles would be difficult to measuredirectly (with a protractor, for example), but the geometry indicated in Figure 1shows you how to determine the angles by distance measurements.

Hint: The distance from the central bright spot to the place where the direct beam strikesthe wall is 02y (see Figure 1).

(d)Make measurements as needed to determine 0 , 1 , 2 , and 3 , then use

Equation (3) to determine the wavelength of the laser light. Also estimate theuncertainty in your value for the wavelength.

Part II: Determining the Amount of Data on a CD

Now that you have measured the wavelength of the laser using a ruler, you can use the laseras a ruler to measure the spacing between tracks on a compact disc (CD)! From this, youmay determine the maximum amount of information that can be stored on a CD.

CD diffraction

The surface of a CD is a highly reflective layer containing a spiral path of small marks, orpits. If stretched out, this spiral would be about 5 km long! The digital data are stored in acode, according to the pit length and the distance between pits. [Imagine an advanced style ofMorse Code: dot-dash etc.] The pits are arranged along the spiral path in tracks, as shown inFigure 3. A portion of one track is highlighted by the white box. The depth of each pit is 0.11m and the width is 0.5 m. Pit length and spacing varies, as can be seen, but the averagespacing from pit to pit is roughly the same size as the distance between the tracks of pits.


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The tracks of pits and the unbroken stripes between them behave in much the same way as areflective diffraction grating, but here the stripes curve gradually around the CD within therecording area (Figure 3). The fine stripes are why you see beautiful rainbow colors whenwhite light illuminates the CD.

However, when light of one wavelength (here, a laser beam) is reflected off the disc, adiffraction pattern is formed. If the angle of incidence is close to the normal, the condition forconstructive interference is identical to that for a transmission diffraction grating (seeEquation 1). In the present example, the rows of pits (tracks) make the grating, and thedistance between the rows of pits, d, can be determined from Equation 1.

By measuring and using your value of from Part I, you can use Equation (1) to calculatethe distance between rows of pits. The experimental arrangement is illustrated in Figure 4.

Measurement procedure

(a)Arrange a disc, laser, and screen in a manner similar to Figure 4a. Direct thelaser beam such that it strikes the CD approximately half way up, as shown inFigure 4b. Adjust the angle between the laser beam and the CD until the directmirror reflection (n= 0) comes back to hit the front of the laser pointer (you mayneed to have it hit 2-3mm above where it comes out, in order to see it). Doingthis will insure that the incident laser beam is normal to the surface of the CD.

You should be able to see the first-order maximum (bright spot) on the screen.

data recording area

Figure 3

Photograph of pits on a CD. FromOn the Surface ofThings, by Felice Frankel and George Whitesides.


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(b)Measure distances as needed to determine the angle of the first-order maximum(bright spot), then calculate the spacing dfrom Equation (1).

laser

screen

CD

CD

laser

beam

Figure 4a 4b

Information stored on a CD

Now calculate the maximum amount of information (number of pits or, literally, bits ofinformation) that can be put on a CD.

(c)First, calculate the area occupied by one bit, using the simple model that itoccupies a rectangle of width dand length l. To simplify things, assume that, onaverage, lis equal to d.

(d)Now calculate the area of the CD that is actually recorded with data. You willneed to measure the radii of the circles defining the recorded area on your CD,

and remember that the area of a circular band is the difference of the areas of thelarge and small circles.

The total number of bits that can be recorded is then the total recorded area divided by thearea for each bit. How many bits can be stored on the CD?

Data amounts are more often given in bytes, where 1byte = 8 bits. Also, 1 MB = 1 megabyte

= 610 bytes. Based on your simple model and your measurements, how many megabytes canbe stored on the CD?

The actual amount of storage on a CD is about 650 to 700MB.


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Additional comments

You may be interested to know that the table of contents for the whole CD is recorded on thelead-in portion consisting of about 30 tracks (one track equals one trip around the disc). The

width of this program area corresponds to the thickness of one human hair. To detectindividual pits, the laser beam must be focused down to a spot about 1m in diameter. Thisshould give you an idea of how remarkably spatially coherent the light is and an appreciationfor the technological obstacles that must be overcome to track these bits of information. TheCD player is literally operating at the diffraction limit (resolution) of light! And now wehave DVD discs! Check the table below for a comparison between DVD and CD discs.

Specifications CD DVD

Disc Diameter 120 mm 120 mm

Disc thickness 1.2 mm 1.2 mm

Disc structure Single substrate Two bonded 0.6mmsubstrates

Laser wavelength 780 nm (infrared) 650 and 635 nm (red)

Numerical aperture 0.45 0.60

Track pitch 1.6 m 0.74 m

Shortest pit/land length .83 m 0.4 m

Data layers 1 1 or 2

Data capacity 680 megabytes Single layer 4.7 gigabytesDual layer 8.5 gigabytes

Data rate Data rate 165 kilobytes/sec Data rate 1,000 kilobytes/sec

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