4 For three experiments, Fig. 36-31 givesa versus angle e in one-slit diffraction usinglight of wavelength 500 nm. Rank the ex-periments according to (a) the slit widthsand (b) the total number of diffractionminima in the pattern, greatest first.

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Answered: 4 For three experiments, Fig. 36-31…

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Chapter4: Diffraction

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Problem 31P: A single slit of width 0.1 mm is illuminated by a mercury light of wavelength 576 nm. Find the...

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A monochromatic light of wavelength 589 nm incident on a double slit with slit width 2.5 m and unknown separation results in a diffraction pattern containing nine interference peaks inside the central maximum. Find the separation of the slits.
Figure 27.56 shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where sin, with in radians), the distance between fringes is given by y=x/d. Figure 27.56 The distance between adjacent fringes is y=x/d, assuming the slit separation d is large compared with .
Check Your Understanding Although m, the number of fringes observed, is an integer, which is often regarded as having zero uncertainty, in practical terms, it is all too easy to lose track when counting fringes. In Example 3.6, if you estimate that you might have missed as many as five fringes when you reported m=122 fringes, (a) is the value for the index of refraction worked out in Example 3.6 too large or too small? (b) By how much?
A single slit of width 0.1 mm is illuminated by a mercury light of wavelength 576 nm. Find the intensity at a 10° angle to the axis in terms of the intensity of the central maximum.
In a thermally stabilized lab, a Michelson interferometer is used to monitor the temperature to ensure it stays constant. The movable mirror is mounted on the end of a 1.00-m-long aluminum rod, held fixed at the other end. The light source is a He Ne laser, =632.8 nm . The resolution of this apparatus corresponds to the temperature difference when a change of just one fringe is observed. What is this temperature difference?
On a certain crystal, a first-order X-ray diffraction maximum is observed at an angle of 27.1° relative to its surface, using an X-ray source of unknown wavelength. Additionally, when illuminated with a different, this time of known wavelength 0.137 nm, a second-order maximum is detected at 37.3°. Determine (a) the spacing between the reflecting planes, and (b) the unknown wavelength.
Calculate the wavelength of light that produces its first minimum at an angle of 36.9° when falling on a single slit of width 1.00 m.
A 5.08-cm-long rectangular glass chamber is inserted into one arm of a Michelson interferometer using a 633-nm light source. This chamber is initially filled with air (n=1.000293) at standard atmospheric pressure but the air is gradually pumped out using a vacuum pump until a near perfect vacuum is achieved. How many fringes are observed moving by during the transition?
A single slit of width 0.10 mm is illuminated by a mercury lamp of wavelength 576 nm. Find the intensity at a 10° angle to the axis in terms of the intensity of the central maximum.
Show that a diffraction grating cannot produce a second-order maximum for a given wavelength of light unless the first-order maximum is at an angle less than 30.0°.
A parallel beam of light containing orange (610 nm) and violet (410 nm) wavelengths goes from fused quartz to water, striking the surface between them an a 60.0° incident angle. What is the angle between the two colors in water?
A film of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths? Oil has an index of refraction of 1.40.

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4 For three experiments, Fig. 36-31 gives a versus angle e in one-slit diffraction using light of wavelength 500 nm. Rank the ex- periments according to (a) the slit widths and (b) the total number of diffraction minima in the pattern, greatest first.