PHYSICS 1040L LAB LAB 7: DIFFRACTION & INTERFERENCE

Transcription

1 PHYSICS 1040L LAB LAB 7: DIFFRACTION & INTERFERENCE Object: To investigate the diffraction and interference of light, Apparatus: Lasers, optical bench, single and double slits. screen and mounts. Theory: On the basis of geometrical ray theory, an opening in an object illuminated by parallel rays of light should have a sharp image the same size and shape as the opening as indicated in Figure 1. What we see, however, is an image somewhat larger than the opening whose edges are not sharply defined. Similarly, the shadow of an object placed in the path of parallel light is not sharply defined. This Figure 1. Image predicted by Ray Theory is due to the fact that light is a wave motion and each point on the edge of the object acts as a new source of light. The light moves with a spherical wave front from these points which makes the edges of the shadow appear "fuzzy" as some of this light falls in the shadow of the -parallel light. This phenomenon is known as diffraction. The faint illumination in a darkened room from a bright

2 Figure 2. Wave motion of light frequently observed example of this effect The light is diffracted by the small gap at the bottom of the closed door. If a small opening or sift is illuminated, one will observe a pattern of light on a screen which consists of a central bright region flanked by alternating dark and successively dimmer regions on either side. The width of the central bright region is twice the width of the other, dimmer, regions. Figure 3. Intensity Pattern of single slit diffraction This is called the Fraunhofer diffraction of a single slit. Since each portion of the slit acts as a source of spherical waves (Huygen's principle), light from one portion of the slit may interfere, constructively or destructively, with that from another portion to produce the observed pattern. In Figure 11, the circles represent crests of the spherical waves. Note that constructive interference will occur at points on the screen where the lights from different parts of the slit have path lengths differing by an integral number of wavelengths. A plot of the relative intensity versus the angle of deviation for this pattern is shown- in Figure I 11. The angular position of the dark portions of this pattern is given by:

3 n λ = a sin(φ) (Eq. 1), where λ is the wavelength of the light, a is the width of the slit, φ is the angular deviation, and n = 1, 2, 3... If the barrier has two openings separated by a distance, d, we will also observe a pattern of equally spaced light and dark spots. The spacing of the bright spots is given by an expression similar to Eq. 1: mλ = d sin(θ) (Eq. 2), where θ is the angular deviation of the bright spots and m = 1, 2, 3. Since each of the double slits is also a single slit, the patterns from the two phenomena will be superimposed. Bearing in mind that Eq. 1 represents the positions of the minima from the single slit pattern and that Eq. 2 represents the position of the maxima from the double slit pattern, there should be points in the distribution in which the two patterns will destructively interfere with other, designated by the lines D in figure IV. This will occur when the angles θ and ϕ are equal and the separation of the two slits is an integral multiple of the slit widths. This can be shown by dividing Equation 2 by Equation 1 giving: m/n = d/a Figure 4. Double slit interference

4 If the slit separation is four times the slit width, for example, destructive interference will occur when m = 4, 8, The resultant pattern of intensities for the central region of a double slit is shown in Figure V. The upper curve represents the single slit pattern while the lower curve represents the distribution within the central curve. Each of the peaks in the upper curve will have a similar distribution (not shown). Figure 5. Intensity pattern for double slit interference Procedure and Data analysis Warning: Laser beams may cause permanent vision impairment or blindness. Do NOT allow the laser beam (or its reflection) to point into anybody's eye. To avoid stray beams in the laboratory, make sure beams from your laser terminate on a screen at all times. Laser beams are extremely intense compared to light from any common light source (even compared to sunlight, as viewed from earth). Permanent blindness may result from prolonged exposure to any laser beam, even those from small laser pointers. 1. Place the Diode Laser on the optical bench. Place the single slit slide in front of the laser on the mount. Place the screen on the other mount and place it near the opposite end on the optical bench. 2. Illuminate a 0.02 mm single slit with laser light. Adjust the position of the slit and the laser so that the laser light is on the screen. Record the width of the central maximum. From the minimum (Dark area) on one side of the central maximum to the dark area on the other side. See Figure 8. Measure the distance from the slit slide to the front of the screen and record it in your data table.

5 Figure 6. Examples of single slit slides double slit slides, and aperture and diffraction patterns. Slide single slits: widths 0.02, 0.04, 0.08, 0.16 mm. Slide sets of double slits: slit widths 0.04 and 0.08 mm; slit spacing 0.25 and 0.5 mm. Slide sets of multiple slits: 2, 3, 4, 5 slits; all widths 0.04 mm; all spaced mm. Slide 4 -- Apertures: 2 circular apertures 0.04, 0.08 mm dia.; 1 array of equilateral triangular apertures; 1 array of square apertures Figure 7 Close-up a double slit slide. NOTE: It might not be like the ones we are using. Look at the labels on your slides.

6 Figure 8. Single Slit Pattern 3. Repeat Step 1 with the 0.04 mm, 0.08 mm slits. 4. What relationship, if any, do you observe between the slit widths and widths of the central maxima? Record your observations in your results section your report. Is the relationship directly or inversely proportional? 5. Determine the wavelength of the laser light from Equation 1, using each one of the three observations. Find the average of the wavelength λ in your data table. Find the % error of the experimental value of λ from the wavelength of the laser as marked on the laser itself. 6. Choose one set of double slits with the same slit width and different slit separation: Choose the slit width of 0.04 mm; slit spacing of 0.25 and 0.5 mm. Record the slit width and separations your data table. 7. Illuminate each of the double slits and measure the measure the width of the central maximum, 2y0. (See your data page for the diagram. Also see Figure 10 and 16). Is there any correspondence between the pattern you observe and the single slit patterns you measured? Make sure the laser light goes through both slits. If it does not you are just repeating the single slit experiment. By inspection, make sure both slits are illuminated approximately equally. Adjust the positions so that you clearly observe an interference pattern on the screen.

7 Figure 9. Comparison of Single Slit and Double slit image. Figure 10. Comparison of Single Slit and Double slit patterns for different values of Slit Width and Separation than in Figure Temporarily remove the screen and using a piece of white paper, move it farther away until you can count the number of bright fringes.

8 9. Calculate the wavelength of the laser light for each silt separation using Equation 2. Find the average wavelength and record the result in your data table. How does this agree with the calculation from Equation 1? Calculate the % error in the experimental wavelength for this method. 10. How does the number of bright fringes vary with slit separation? Record your observations in the results section of your report. 11. Illuminate holes of different shapes and sizes and sketch the patterns observed. Explain the process by which these patterns are formed. Figure11.Diode Laser

9 Figure 12. DIODE LASER ON OPTICAL BENCH

10 Figure 13. BACK SIDE OF DIODE LASER Figure 14. HOW COLOR (WAVELNGTH) Changes Double Slit Interference

11 Figure 15. PASCO 1m ADVANCED OPTICS BENCH Figure 16. SINGLE SLIT DIFFRACTION PATTERN

12 Figure 17. DOUBLE SLIT INTEFERENCE PATTERN

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