EXPERIMENT NO. 405 DIFFRACTION
JEROMMEL OLGADO, PHY13L/A2
[email protected]
Abstract
The experiment deals with the study of diffraction specifically with single slit diffraction and two slit interference. The objectives of this experiment are: to explore the phenomenon of diffraction of light, and to compare single slit diffraction and two slit interference. The experiment is divided into three parts. The first part is the analysis of single slit diffraction by determining the positions of dark fringes, and the s econd part is the analysis of two slit interference by measuring the positions of the bright fringes. With the gathered data and observation, the single slit diffraction and two slit interference under the concept of diffraction with the use of diode laser, slit disk holders, and an optical bench with screen is interpreted and further understood and analyzed by physical experiment which is then discussed and explained in this paper. Key Words: Diffraction, Single slit diffraction, two slit interference, light bend Introduction
Everyone is used to the idea that sound bends around corners. If sound didn’t behave this way, you couldn’t hear a police siren that’s out of sight around a corner or the speech of a person whose back is turned to you. What may surprise you, and certainly surprised many scientists of the early 19th century, that light can bend around corners as well. When light from a point source falls on a straightedge and casts a shadow, the edge of the shadow is never perfectly sharp. Some light appears in the area that we expect to be in the shadow, and we find alternating bright and dark fringes in the illuminated area. In general, light emerging from from apertures doesn’t behave precisely according to the predictions of the straight -line ray model of geometric optics. We can analyze diffraction patterns using Huygen’s principle. This principle states that we can consider every point of a wave front as a source of secondary wavelets. These spread out in all directions with a speed equal to the speed of propagation of the wave. The position of the wave front at any later time is the envelope of the secondary secondar y wavelets at that t hat time. To find the resultant displacement at any point, we combine all the individual displacements produced by these secondary waves, using the superposition principle and taking to account their amplitudes and relative phases.
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Methodology 1. Materials
The Experiment made use of the following materials: 1 pc optical bench with screen, 1 pc diode laser, 1 pc single slit disk with holder, 1 pc multiple slit disk with holder, and 1 pc ruler. The materials can be seen in Fig. 1.
Fig. 1: Materials. Names are listed above.
2. Procedure 2.1. Single Slit Diffraction
After the set-up is done, turn the single slit disk until the laser is incident on the single slit of width 0.16mm. Using a ruler, determine the middle central bright fringe of the diffraction pattern formed on the screen. This will be position y=0 with the y-axis along the line of the diffraction pattern. From y=0, determine the positions of the dark fringes: y 1, y2, y3, y-1, y-2, y-3. Move the screen to the 85cm mark and determine the positions of the dark fringes and the repeat the same with the screen moved to the 70cm mark. Move the screen back to the 100cm mark and repeat the procedure for slit widths 0.08mm and 0.04mm.
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2.2. Two Slit Interference
From the set-up of 2.1, Replace the single slit disk with the multiple slit disk; like the single slit disk, the multiple slit disk should be facing the diode laser. Turn on the diode laser and turn the disk until the laser is incident on the double slit marked 0.08/0.50. The diode laser should be perfectly centered on the double slit so that a clear pattern may be formed. If not centered, adjust the knobs of the diode laser. Next, determine the middle of the central bright fringe using a ruler. This will be position y=0, with the y-axis along the line of the interference pattern. From y=0, determine the positions of the bright fringes: y 1, y2, y3, y-1, y-2, y-3. . Move the screen to the 85cm mark and determine the positions of the bright fringes and the repeat the same with the screen moved to the 70cm mark. Move the screen back to the 100cm mark and repeat the procedure for the double slits marked 0.08/0.25 mm and 0.04/0.5. 3. Set-Up
Fig. 2: Screen at 100cm mark, diode laser at 0cm mark pointed at the screen, And the single slit disk at the 10cm mark.
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Results and Discussion
The fifth experiment is all about diffraction of light waves. For this experiment our main objective is to explore the phenomenon of diffraction of light and to compare single slit diffraction and multiple slits interference. 4.1 Determination of Index of Refraction of Glass
To start, we first investigate the single slit diffraction. In order for us to investigate the diffraction occurring in a single slit disk, we try to change either the slit-screen difference, x, or slit width, a, leaving or setting the other variable as constant. From here, we can get the value f or wave length, λ, and eventually analyze its relationship to the slit-screen difference, x, and the Slit width, a. Based on the results of our experiment, I observed that for every increase in the slit-screen distance, x, corresponds to a decrease in the wave length, λ. On the other hand, I observed that at constant slit-screen separation, an increase in slit width, a corresponds to an increase in value with regards to the wave length, λ. Based on the results of our observations, we can conclude that the results are consistent with the theory which gives the equation, λ=(yma)/(mx) where a is the slit width and x is the slit-screen separation. With that, we observed that the waves are 180 o since we’ve used a single slit disk and therefore resulting to a destructive interface. Destructive interface occurs when a crest of one wave overlaps through another wave resulting to a decrease in amplitude and formation of a dark region known as the central minimum. The single slit formation can be found in the figure below and the data obtained in this part are shown on TABLE 1. TABLE 1. SINGLE SLIT DIFFRACTION a = 0.16 mm
m 1 2 3 -1 -2 -3
m 1 2 3 -1 -2 -3
m
x = 90 cm Calculated λ 711 nm 622 nm 652 nm -711 nm -622 nm -652 nm 668 nm x = 75 cm Calculated λ 640 nm 747 nm 640 nm -640 nm -747 nm -640 nm 676 nm x = 60 cm Calculated λ
ym 0.4 cm 0.6 cm 1.1 cm -0.4 cm -0.6 cm -1.1 cm AVERAGE CALCULATED λ a = 0.16 mm ym 0.3 cm 0.7 cm 0.9 cm -0.3 cm -0.7 cm -0.9 cm AVERAGE CALCULATED λ a = 0.16 mm ym 4
1 2 3 -1 -2 -3
m 1 2 3 -1 -2 -3
m 1 2 3 -1 -2 -3
m 1 2 3 -1 -2 -3
m 1 2 3 -1 -2 -3
m 1
0.2 cm 0.6 cm 0.7 cm -0.2 cm -0.6 cm -0.7 cm AVERAGE CALCULATED λ a = 0.08 mm ym 0.8 cm 1.5 cm 2.2 cm -0.8 cm -1.5 cm -2.2 cm AVERAGE CALCULATED λ a = 0.08 mm ym 0.7 cm 1.2 cm 1.8 cm -0.7 cm -1.2 cm -1.8 cm AVERAGE CALCULATED λ a = 0.80 mm ym 0.5 cm 1.0 cm 1.5 cm -0.5 cm -1.0 cm -1.5 cm AVERAGE CALCULATED λ a = 0.04 mm ym
533 nm 800 nm 622 nm -533 nm -800 nm -622 nm 677 nm x = 90 cm Calculated λ 711 nm 667 nm 652 nm -711 nm -667 nm -652 nm 567.90 nm x = 75 cm Calculated λ 747 nm 640 nm 640 nm -747 nm -640 nm -640 nm 676 nm x = 60 cm Calculated λ 667 nm 667 nm 667 nm -667 nm -667 nm -667 nm 667 nm
x = 90 cm Calculated λ 577.78 nm 555.55 nm 548.15 nm 533.33 nm 533.33 nm 533.33 nm
667 nm 667 nm 667 nm -667 nm -667 nm -667 nm
AVERAGE CALCULATED λ a = 0.04 mm ym
667 nm
x = 75 cm Calculated λ
1.3 cm
693 nm
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2 3 -1 -2 -3
m 1 2 3 -1 -2 -3
2.5 cm
667 nm
3.8 cm
676 nm
-1.3 cm
-693 nm
-2.5 cm
-667 nm
-3.7 cm
-676 nm
AVERAGE CALCULATED λ a = 0.04 mm ym
679 nm
x = 60 cm Calculated λ
1 cm
667 nm
2 cm
667 nm
3 cm
667 nm
-1 cm
-667 nm
-2 cm
-667 nm
-3 cm
-667 nm
AVERAGE CALCULATED λ
667 nm
Fig. 3: Image formed on the screen with a single slit with of 0.16mm And diode laser 100cm away from the screen. 4.2 Two Slit Interference
For the second and the last part of the experiment, the same procedure was done as that of the first part but a multiple slit disk was used instead of the single slit disk. The result of the experiment shows that the observation on the first part is almost the same as the second 6
part. Since we’ve used double-slit disk, waves were in phase resulting to a constructive interference which occurs when crest of the two waves overlap resulting to an increase in amplitude and formation of bright region known as the central maximum. The data obtained in this part are shown on TABLE 2.
TABLE 2. TWO SLIT INTERFERENCE a = 0.08 mm / d = 0.50 mm m ym 0 0.0 cm 1 0.1 cm 2 0.2 cm 3 0.4 cm -1 -0.1 cm -2 -0.2 cm -3 -0.4 cm AVERAGE CALCULATED λ a = 0.80 mm / d = 0.50mm m ym 0 0.0 cm 1 1 cm 2 2 cm 3 3 cm -1 -1 cm -2 -2 cm -3 -3 cm AVERAGE CALCULATED λ
x = 90 cm
Calculated λ 0 nm 667 nm 667 nm 648 nm -667 nm -667 nm -648 nm 660 nm
x = 75 cm
Calculated λ 0 nm 667 nm 667 nm 667 nm -667 nm -667 nm -667 nm 667nm
a = 0.08 mm / d = 0.50 mm ym
x = 60 cm Calculated λ
M 0 0.0 cm 1 0.8 cm 2 1.7 cm 3 2.3 cm -1 -0.8cm -2 -1.7 cm -3 -2.3 cm AVERAGE CALCULATED λ a = 0.08 mm / d = 0.25 mm m ym 0 0.0 cm 1 2.3 cm 2 4.8 cm 3 7.3 cm -1 -2.3 cm
0 nm 667 nm 708 nm 639 nm -667 nm -708 nm -639 nm 670 nm
x = 90 cm
Calculated λ 0 nm 639 nm 667 nm 676 nm -639 nm
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-2 -4.8 cm -3 -7.3 cm AVERAGE CALCULATED λ a = 0.08 mm / d = 0.25 mm M ym 0 0.0 cm 1 1.9 cm 2 4.1 cm 3 6.1 cm -1 -1.9 cm -2 -4.1 cm -3 -6.1 cm AVERAGE CALCULATED λ a = 0.08 mm / d = 0.25 mm 0.0 cm m 1.5 cm 0 3.2 cm 1 4.9 cm 2 -1.5 cm 3 -3.2 cm -1 -4.9 cm -2 0.0 cm -3 AVERAGE CALCULATED λ a = 0.04 mm / d = 0.50 mm m ym 0.0 cm 0 1.2 cm 1 2.3 cm 2 3.5 cm 3 -1.2 cm -1 -2.3 cm -2 -3.5 cm -3 AVERAGE CALCULATED λ a = 0.04 mm / d = 0.50 mm m ym 0.0 cm 0 1 cm 1 2 cm 2 3 cm 3 -1 cm -1 -2 cm -2 -3 cm -3 AVERAGE CALCULATED λ a = 0.04 mm / d = 0.50 mm m ym 0.0 cm 0 0.7 cm 1
-667 nm -676 nm 660 nm
x = 75 cm
Calculated λ 0 nm 633 nm 683 nm 678 nm -633 nm -683 nm -678 nm 665.81 nm
x = 60 cm
Calculated λ 0 nm 625 nm 667 nm 681 nm -625 nm -667 nm -681 nm 637 nm
x = 90 cm
Calculated λ 0 nm 667 nm 639 nm 648 nm -667 nm -639 nm -648 nm 651 nm
x = 75 cm
Calculated λ 0 nm 667 nm 667 nm 667 nm -667 nm -667 nm -667 nm 667 nm
x = 75 cm
Calculated λ 0 nm 583 nm
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1.6 cm 2 2.5 cm 3 -0.7 cm -1 -1.6 cm -2 -2.5 cm -3 AVERAGE CALCULATED λ
668 nm 694 nm -583 nm -668 nm -694 nm 648 nm
As a whole, single and double slit disk differ on their interference but the relationship regarding slit width, wave length and slit-screen separation are all the same. Diffraction depends only on the ratio of wave length to the size of the diffracting object.
Conclusion
Diffraction refers to various phenomena associated with wave propagation such as bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. Even though Diffraction always occurs, its affects generally most noticeable for waves were the wavelength is on order of the diffracting objects. The complex patterns in the intensity of a diffracted wave are for result of interference between different parts of a wave that traveled to the observer by different paths. The angular spacing of the features in the diffraction angle is inversely proportional to the dimensions of the objects causing the diffraction. The diffraction angles are invariant under scaling; they depend only on the ratio of the wavelength to the size of the diffracting object. The effects of diffraction can be easily seen in everyday life. The closed space tracks on a CD act as a diffracting grating to form a rainbow pattern we seen when looking at the disk. Diffraction in the atmosphere by small particles in it can cause a bright ring to be visible around a bright light source like the sun or the moon. Diffraction can also be a concern in some technical applications; it sets a Fundamental limit to the resolution of camera, telescope or microscope. Interference is the overlapping of two waves. It is a phenomenon which occurs when two waves of the same nature from different sources meet at the same place. Constructive interference when ting amplitude is greater than the amplitude of the two waves that results to the formation of bright region known as the centr al maximum. On the other hand, Destructive interference occurs when the crest of one wave overlaps the trough of another wave resulting to a decrease in amplitude and the formation of dark region known as the central minimum.
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References
Book [1] Halliday, Principles of Physics, 9e., John Wiley & Sons, Inc., Asia (2011). [2] Young,H., University Physics with Modern Physics 12e., Pearson Education, Inc., San Francisco (2008) [3] Mapua Institute of Technology, Physics 4 Lab Manual., Department of Physics., nd.
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