experiment 23: wave optics - phy.olemiss.edu€¦ · 136 experiment 23: wave optics advance reading...

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Experiment 23: Wave Optics Figure 23.1: Diraction and Interference Not to scale: For optimal measuring, distance between the slide holder and measuring surface should be at least 1 meter. EQUIPMENT Laser Black Felt Single-Slit Slide Double-Slit Slide Slide Holder Meter Stick Vernier Caliper Clipboard, Paper (Screen) (1) Flashlight per person 133

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Page 1: Experiment 23: Wave Optics - phy.olemiss.edu€¦ · 136 Experiment 23: Wave Optics Advance Reading Text: Wave optics, wavelength, frequency, electromag-netic spectrum, di↵raction,

Experiment 23: Wave Optics

Figure 23.1: Di↵raction and Interference

Not to scale: For optimal measuring, distance betweenthe slide holder and measuring surface should be at least 1 meter.

EQUIPMENT

LaserBlack FeltSingle-Slit SlideDouble-Slit SlideSlide HolderMeter StickVernier CaliperClipboard, Paper (Screen)(1) Flashlight per person

133

Page 2: Experiment 23: Wave Optics - phy.olemiss.edu€¦ · 136 Experiment 23: Wave Optics Advance Reading Text: Wave optics, wavelength, frequency, electromag-netic spectrum, di↵raction,

134 Experiment 23: Wave Optics

Figure 23.2: Intensity vs. Angle (Di↵raction; Single-Slit)

Note the central envelope of the di↵raction pattern. It is about twice the width of the envelopes on either side. Thepattern repeats with decreasing intensity (dimmer) as the angle increases left or right of ✓ = 0�.

“W” is measured from the center of the dark to the center of the dark on either side of the central envelope.

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Experiment 23: Wave Optics 135

Figure 23.3: Intensity vs. Angle (Interference, Double-Slit)

Note the interference pattern (bright/dark fringes) contained within the envelopes of the di↵raction pattern. Thecentral envelope is about twice the width of envelopes on either side. The patter repeats with decreasing intensityas the angle increases left or right of ✓ = 0�.

“m” is the order number of each bright fringe. m equals zero when ✓ = 0�; m is symmetric about ✓ = 0�. You willmake a mark through the center of each bright fringe in the central envelope. There is, of course, an odd number offringes in the central envelope. Use Eq. 23.4 to determine m for calculations of �.

Page 4: Experiment 23: Wave Optics - phy.olemiss.edu€¦ · 136 Experiment 23: Wave Optics Advance Reading Text: Wave optics, wavelength, frequency, electromag-netic spectrum, di↵raction,

136 Experiment 23: Wave Optics

Advance Reading

Text: Wave optics, wavelength, frequency, electromag-netic spectrum, di↵raction, interference, principle ofsuperposition.

Objective

The objective of this experiment is to study di↵ractionand interference and to determine �, the wavelength ofthe laser light.

Theory

Single-Slit Di↵raction

Light passing through a narrow slit (slit width, D)will produce a di↵raction pattern. The di↵raction pat-tern consists of a series of light and dark bands, orenvelopes.

Fig. 23.2 shows a plot of the light intensity vs. angle inthe di↵raction pattern. The slit width, D, is providedon the slide; �D = 0.005 mm. We use the small angleapproximation to derive Eq. 23.1; this method requiresangles in radians. The central bright envelope of thedi↵raction pattern subtends an angle of 2�, where:

� =�

D(23.1)

and � is the wavelength. The angle will not be mea-sured directly. � can be determined by first measuringthe distance from the slit to the screen (L), then mea-suring the width of the central envelope, marked as Win Fig. 23.2.

2 tan� =W

L(23.2)

Using substitution, Eq. 23.1 and Eq. 23.2 are solvedfor �, in terms of quantities that can be determined inthe lab: W , D, L. The distance L should be at least1 m for both di↵raction and interference procedures.

Double-Slit Interference

When coherent light (e.g., laser light) passes throughtwo narrow slits that are close together, an interfer-ence pattern will result. The two slits are treated asif they are two points sources of coherent light. Thispattern results from the addition and cancellation oflight waves from the two slits, known as constructiveand destructive interference, respectively. The result-ing bands of light (conversely, bands of darkness) arereferred to as bright fringes (or dark fringes).

Figure 23.4: Double Slit - Path Length Di↵erence

Constructive interference occurs when the path lengthdi↵erence, �, is equal to an whole number of wave-lengths (i.e., even number of 1

2

-wavelengths). Destruc-tive interference occurs when � is an odd number of1

2

-wavelengths.

Constructive interference occurs when � = m�. Pathlength di↵erence is necessarily: � = d sin ✓, where d isslit spacing.

� = d sin ✓ = m� (23.3)

where m = 0, 1, 2, . . . , with m = 0 being the cen-tral maximum fringe. The fringe order number can befound by counting the number of fringes:

m =#fringes� 1

2(23.4)

For small angles measured in radians, the small angleapproximation (refer to Experiment 11) is useful:

sin ✓ ⇡ tan ✓ = y/L (23.5)

Using substitution, Eq. 23.3 and Eq. 23.5 are solvedfor �, in terms of quantities that can be determined inthe lab: m, d, y, L.

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Prelab 23: Wave Optics 137

Name:

1. Define di↵raction. (10 pts)

2. Define interference. (10 pts)

3. What does the symbol D in Eq. 23.1 represent? (10 pts)

4. What does the symbol d in Eq. 23.3 represent? (10 pts)

5. Use substitution to solve the single-slit equations (Eq. 23.1 and Eq. 23.2) for �, in terms of the quantities that wewill determine in lab: W , L, D. (20 pts)

6. Use substitution to solve the double-slit equations (Eq. 23.5 and Eq. 23.3) for �, in terms of the quantities thatwe will determine in lab: m, L, d, y. (20 pts)

7. Given D1

= .02 mm and �D = .005 mm, calculate �%

D1

. Given D2

= .16 mm, calculate �%

D2

. Why will it beimportant to begin with the widest slit? (20 pts)

Page 6: Experiment 23: Wave Optics - phy.olemiss.edu€¦ · 136 Experiment 23: Wave Optics Advance Reading Text: Wave optics, wavelength, frequency, electromag-netic spectrum, di↵raction,

138 Experiment 23: Wave Optics

PROCEDURE

PART 1: Single-Slit Di↵raction

1. Place the single-slit slide on the slide holder. Alignthe slide holder in front of the laser aperture.

2. Set up the clipboard and paper in front of thelaser, at least one meter away from the slide holder.Record this distance, L.

3. Turn on the laser to create a di↵raction patternon the clipboard. Begin with the widest slit. Slitwidth is provided on the slide; its uncertainty is�D = ±0.005 mm.

4. Mark the width, W , of the central band. Measurefrom the center of the dark bands on either side.Take measurements in a tidy manner, use extra pa-per as needed.

5. Close the shutter. Calculate �; show your work.[The mathematical model uses radians.]

6. Repeat for the three remaining slits. Calculate av-erage �

ss

for the single-slit procedure.

PART 2: Double-Slit Interference

7. Place the double-slit slide on the holder. Turn onthe laser. Begin with the widest spacing.

8. Mark a line through each of the bright fringes in thecentral bright envelope. The distance between theoutermost fringes is 2y.

9. Close the shutter. Determine 2y and m.

10. Calculate �. Show your work.

11. Repeat for the remaining pairs of slits. Calculateaverage �

ds

for the double-slit procedure.

12. Calculate the total average � from your measure-ments. Compare this to the laser’s theoretical wave-length: � = 6328 A [A=10-10 m]. Show your work.

QUESTIONS

1. Explain and compare di↵raction and interference.

2. What are the sources of uncertainty in this experi-ment?