Two coherent light sources

1. Two coherent light sources

2. Q35.1 Two sources S1 and S2 oscillating in phase emit sinusoidal waves. Point P is 7.3 wavelengths from source S1 and 4.3 wavelengths from source S2. As a result, at point P there is A. constructive interference. B. destructive interference. C. neither constructive nor destructive interference. D. not enough information given to decide.

3. A35.1 Two sources S1 and S2 oscillating in phase emit sinusoidal waves. Point P is 7.3 wavelengths from source S1 and 4.3 wavelengths from source S2. As a result, at point P there is A. constructive interference. B. destructive interference. C. neither constructive nor destructive interference. D. not enough information given to decide.

4. Q35.2 Two sources S1 and S2 oscillating in phase emit sinusoidal waves. Point P is 7.3 wavelengths from source S1 and 4.6 wavelengths from source S2. As a result, at point P there is A. constructive interference. B. destructive interference. C. neither constructive nor destructive interference. D. not enough information given to decide.

5. A35.2 Two sources S1 and S2 oscillating in phase emit sinusoidal waves. Point P is 7.3 wavelengths from source S1 and 4.6 wavelengths from source S2. As a result, at point P there is A. constructive interference. B. destructive interference. C. neither constructive nor destructive interference. D. not enough information given to decide.

6. Interference from two radio stations • Radio station operating at 1500 kHz has two antennas spaced 400m apart. In which directions is the intensity greatest in the resulting radiation pattern far away (>> 400m) from the antennas? How many total regions of high intensity are there?

7. As the waves interfere, they produce fringes • A red laser produces the following fringe pattern: • What happens to fringe pattern if the spacing between slits increases? • What happens if you shine a green laser (higher frequency) through the same slits? • What happens if you move the screen farther away from the slits? • Spacing between fringe pattern • A) increases • B) decreases • C) stays the same

8. Q35.3 Coherent light passing through two slits (S1 and S2) produces a pattern of dark and bright areas on a distant screen. If the wavelength of the light is increased, how does the pattern change? A. The bright areas move closer together. B. The bright areas move farther apart. C. The spacing between bright areas remains the same, but the color changes. D. any of the above, depending on circumstances E. none of the above

9. A35.3 Coherent light passing through two slits (S1 and S2) produces a pattern of dark and bright areas on a distant screen. If the wavelength of the light is increased, how does the pattern change? A. The bright areas move closer together. B. The bright areas move farther apart. C. The spacing between bright areas remains the same, but the color changes. D. any of the above, depending on circumstances E. none of the above

10. Q35.4 Coherent light passing through two slits (S1 and S2) produces a pattern of dark and bright areas on a distant screen. What is the difference between the distance from S1 to the m = +3 bright area and the distance from S2 to them = +3 bright area? A. three wavelengths B. three half-wavelengths C. three quarter-wavelengths D. not enough information given to decide

11. A35.4 Coherent light passing through two slits (S1 and S2) produces a pattern of dark and bright areas on a distant screen. What is the difference between the distance from S1 to the m = +3 bright area and the distance from S2 to them = +3 bright area? A. three wavelengths B. three half-wavelengths C. three quarter-wavelengths D. not enough information given to decide

12. Q35.4 Coherent light passing through two slits (S1 and S2) produces a pattern of dark and bright areas on a distant screen. What is the difference between the phase from S1 to the m = +3 bright area and the distance from S2 to them = +3 bright area? A. 3p/2 B. 3p C. 6p D. not enough information given to decide

13. A35.4 Coherent light passing through two slits (S1 and S2) produces a pattern of dark and bright areas on a distant screen. What is the difference between the phase from S1 to the m = +3 bright area and the distance from S2 to them = +3 bright area? A. 3p/2 B. 3p C. 6p D. not enough information given to decide

14. Diffraction grating • What is the first order diffraction peak (angle) for a grating with 600 slits per mm for red (700 nm) and violet (400nm) light? • By what angle is the rainbow spread out for this situation?

15. Fraunhofer diffraction and an example of analysis • A red laser (700nm) is shown through a single slit. • What is the slit width for this diffraction pattern?

16. Q36.1 Light of wavelength l passes through a single slit of width a. The diffraction pattern is observed on a screen that is very far from from the slit. Which of the following will give the greatest increase in the angular width of the central diffraction maximum? A. Double the slit width a and double the wavelength l. B. Double the slit width a and halve the wavelength l. C. Halve the slit width a and double the wavelength l. D. Halve the slit width a and halve the wavelength l.

17. A36.1 Light of wavelength l passes through a single slit of width a. The diffraction pattern is observed on a screen that is very far from from the slit. Which of the following will give the greatest increase in the angular width of the central diffraction maximum? A. Double the slit width a and double the wavelength l. B. Double the slit width a and halve the wavelength l. C. Halve the slit width a and double the wavelength l. D. Halve the slit width a and halve the wavelength l.

18. Intensity maxima in a single-slit pattern • The expression for peak maxima is iterated for the strongest peak. • Consider Figure 36.9 that shows the intensity as a function of angle.

19. Q36.2 In a single-slit diffraction experiment with waves of wavelength l, there will be no intensity minima (that is, no dark fringes) if the slit width is small enough. What is the maximum slit width a for which this occurs? A. a = l/2 B. a = l C. a = 2l D. The answer depends on the distance from the slit to the screen on which the diffraction pattern is viewed.

20. A36.2 In a single-slit diffraction experiment with waves of wavelength l, there will be no intensity minima (that is, no dark fringes) if the slit width is small enough. What is the maximum slit width a for which this occurs? A. a = l/2 B. a = l C. a = 2l D. The answer depends on the distance from the slit to the screen on which the diffraction pattern is viewed.

21. Intensity from single slit

22. Multiple slit interference

23. Several slits • More slits produces sharper peaks

24. Q36.3 In Young’s experiment, coherent light passing through two slits separated by a distance d produces a pattern of dark and bright areas on a distant screen. If instead you use 10 slits, each the same distance d from its neighbor, how does the pattern change? A. The bright areas move farther apart. B. The bright areas move closer together. C. The spacing between bright areas remains the same, but the bright areas become narrower. D. The spacing between bright areas remains the same, but the bright areas become broader.

25. A36.3 In Young’s experiment, coherent light passing through two slits separated by a distance d produces a pattern of dark and bright areas on a distant screen. If instead you use 10 slits, each the same distance d from its neighbor, how does the pattern change? A. The bright areas move farther apart. B. The bright areas move closer together. C. The spacing between bright areas remains the same, but the bright areas become narrower. D. The spacing between bright areas remains the same, but the bright areas become broader.

26. Michelson and Morley’s interferometer • In this amazing experiment at Case Western Reserve, Michelson and Morley suspended their interferometer on a huge slab of sandstone on a pool of mercury (very stable, easily moved). As they rotated the slab, movement of the earth could have added in one direction and subtracted in another, changing interference fringes each time the device was turned a different direction. They did not change. This was an early proof of the invariance of the speed of light.