1. What is the angular separation in second order between light of
wavelengths 400 nm and 600 nm when diffracted by a grating of 5000
grooves/cm? Get solution
2. a. Describe the dispersion in the red wavelength region around 650 nm (both in °/nm and in nm/mm) for a transmission grating 6 cm wide, containing 3500 grooves/cm, when it is focused in the third-order spectrum on a screen by a lens of focal length 150 cm.b. Find the resolving power of the grating under these conditions.Figure 1.... Get solution
3. a. What is the angular separation between the second-order principal maximum and the neighboring minimum on either side for the Fraunhofer pattern of a 24-groove grating having a groove separation of 10−3 cm and illuminated by light of 600 nm?b. What slightly longer (or slightly shorter) wavelength would have its second-order maximum on top of the minimum adjacent to the second-order maximum of 600-nm light?c. From your results in parts (a) and (b), calculate the resolving power in second order. Compare this with the resolving power obtained from the theoretical grating resolving power formula, Eq. (12-11). Get solution
4. How many lines must be ruled on a transmission grating so that it is just capable of resolving the sodium doublet (589.592 nm and 588.995 nm) in the first- and second-order spectra? Get solution
5. a. A grating spectrograph is to be used in first order. If crown glass optics is used in bringing the light to the entrance slit, what is the first wavelength in the spectrum that may contain second-order lines? If the optics is quartz, how does this change? Assume that the absorption cutoff is 350 nm for crown glass and 180 nm for quartz.b. At what angle of diffraction does the beginning of overlap occur in each case for a grating of 1200 grooves/mm?c. What is the free spectral range for first and second orders in each case? Get solution
6. A transmission grating having 16,000 lines/in. is 2.5 in. wide. Operating in the green at about 550 nm, what is the resolving power in the third order? Calculate the minimum resolvable wavelength difference in the second order.Figure 1.... Get solution
7. The two sodium D lines at 5893 Å are 6 Å apart. If a grating with only 400 grooves is available, (a) what is the lowest order possible in which the D lines are resolved and (b) how wide does the grating have to be? Get solution
8. A multiple-slit aperture has (1) N = 2, (2) N = 10, and (3) N = 15,000 slits. The aperture is placed directly in front of a lens of focal length 2 m. The distance between slits is 0.005 mm and the slit width is 0.001 mm for each case. The incident plane wavefronts of light are of wavelength 546 nm. Find, for each case, (a) the separation on the screen between the zeroth- and first-order maxima; (b) the number of bright fringes (principal maxima) that fall under the central diffraction envelope; (c) the width on the screen of the central interference fringe. Get solution
9. A reflection grating is required that can resolve wavelengths as close as 0.02 Å in second order for the spectral region around 350 nm. The grating is to be installed in an instrument where light from the entrance slit is incident normally on the grating. If the manufacturer provides rulings over a 10-cm grating width, determine (a) the minimum number of grooves/cm required; (b) the optimum blaze angle for work in this region; (c) the angle of diffraction where irradiance is maximum (show both blaze angle and diffraction angle on a sketch); (d) the dispersion in nanometers per degree. Get solution
10. A transmission grating is expected to provide an ultimate first-order resolution of at least 1 Å anywhere in the visible spectrum (400 to 700 nm). The ruled width of the grating is to be 2 cm.a. Determine the minimum number of grooves required.b. If the diffraction pattern is focused by a 50-cm lens, what is the linear separation of a 1-Å interval in the vicinity of 500 nm? Get solution
11. A concave reflection grating of 2-m radius is ruled with 1000 grooves/mm. Light is incident at an angle of 30° to the central grating normal. Determine, for first-order operation, the (a) angular spread about the grating normal of the visible range of wavelengths (400 to 700 nm); (b) theoretical resolving power if the grating is ruled over a width of 10 cm; (c) plate factor in the vicinity of 550 nm; (d) radius of the Rowland circle in a Paschen-Runge mounting of the grating.Figure 1.... Get solution
12. How many grooves per centimeter are required for a 2-m radius, concave grating that is to have a plate factor of around 2 nm/mm in first order? Get solution
13. A plane reflection grating with 300 grooves/mm is blazed at 10°.a. At what wavelength in first order does the grating direct the maximum energy when used with the incident light normal to the groove faces?b. What is the plate factor in first order when the grating is used in a Czerny-Turner mounting with mirrors of 3.4-m radius of curvature? Get solution
14. A reflection grating, ruled over a 15-cm width, is to be blazed for use at 2000 Å in the vacuum ultraviolet. If its theoretical resolving power in first order is to be 300,000, determine the proper blaze angle for use (a) in a Littrow mount and (b) with normal incidence.Figure 1.... Get solution
15. Show that the spacing d of the fringes in the formation of a holographic grating, as shown in Figure 12-7c, is given by λ/(2 sin θ), where 2θ is the angle between the coherent beams. If the beams are argon-ion laser beams of wavelength 488 nm and the angle between beams is 120°, how many grooves per millimeter are formed in a plane emulsion (n = 1) oriented perpendicular to the fringes? What is the effect on the fringe separation d of an emulsion with a high refractive index? Get solution
16. A grating is needed that is able, working in first order, to resolve the red doublet produced by an electrical discharge in a mixture of hydrogen and deuterium: 1.8 Å at 6563 Å. The grating can be produced with a standard blaze at 6300 Å for use in a Littrow mount. Find (a) the total number of grooves required; (b) the number of grooves per millimeter on the grating with a blaze angle of 22°12′; (c) the minimum width of the grating. Get solution
17. An echelle grating is ruled over 12 cm of width with 8 grooves/mm and is blazed at 63°. Determine for a Littrow configuration (a) the range of orders in which the visible spectrum (400 to 700 nm) appears; (b) the total number of grooves; (c) the resolving power and minimum resolvable wavelength interval at 550 nm; (d) the dispersion at 550 nm; (e) the free spectral range, assuming the shortest wavelength present is 350 nm. Get solution
2. a. Describe the dispersion in the red wavelength region around 650 nm (both in °/nm and in nm/mm) for a transmission grating 6 cm wide, containing 3500 grooves/cm, when it is focused in the third-order spectrum on a screen by a lens of focal length 150 cm.b. Find the resolving power of the grating under these conditions.Figure 1.... Get solution
3. a. What is the angular separation between the second-order principal maximum and the neighboring minimum on either side for the Fraunhofer pattern of a 24-groove grating having a groove separation of 10−3 cm and illuminated by light of 600 nm?b. What slightly longer (or slightly shorter) wavelength would have its second-order maximum on top of the minimum adjacent to the second-order maximum of 600-nm light?c. From your results in parts (a) and (b), calculate the resolving power in second order. Compare this with the resolving power obtained from the theoretical grating resolving power formula, Eq. (12-11). Get solution
4. How many lines must be ruled on a transmission grating so that it is just capable of resolving the sodium doublet (589.592 nm and 588.995 nm) in the first- and second-order spectra? Get solution
5. a. A grating spectrograph is to be used in first order. If crown glass optics is used in bringing the light to the entrance slit, what is the first wavelength in the spectrum that may contain second-order lines? If the optics is quartz, how does this change? Assume that the absorption cutoff is 350 nm for crown glass and 180 nm for quartz.b. At what angle of diffraction does the beginning of overlap occur in each case for a grating of 1200 grooves/mm?c. What is the free spectral range for first and second orders in each case? Get solution
6. A transmission grating having 16,000 lines/in. is 2.5 in. wide. Operating in the green at about 550 nm, what is the resolving power in the third order? Calculate the minimum resolvable wavelength difference in the second order.Figure 1.... Get solution
7. The two sodium D lines at 5893 Å are 6 Å apart. If a grating with only 400 grooves is available, (a) what is the lowest order possible in which the D lines are resolved and (b) how wide does the grating have to be? Get solution
8. A multiple-slit aperture has (1) N = 2, (2) N = 10, and (3) N = 15,000 slits. The aperture is placed directly in front of a lens of focal length 2 m. The distance between slits is 0.005 mm and the slit width is 0.001 mm for each case. The incident plane wavefronts of light are of wavelength 546 nm. Find, for each case, (a) the separation on the screen between the zeroth- and first-order maxima; (b) the number of bright fringes (principal maxima) that fall under the central diffraction envelope; (c) the width on the screen of the central interference fringe. Get solution
9. A reflection grating is required that can resolve wavelengths as close as 0.02 Å in second order for the spectral region around 350 nm. The grating is to be installed in an instrument where light from the entrance slit is incident normally on the grating. If the manufacturer provides rulings over a 10-cm grating width, determine (a) the minimum number of grooves/cm required; (b) the optimum blaze angle for work in this region; (c) the angle of diffraction where irradiance is maximum (show both blaze angle and diffraction angle on a sketch); (d) the dispersion in nanometers per degree. Get solution
10. A transmission grating is expected to provide an ultimate first-order resolution of at least 1 Å anywhere in the visible spectrum (400 to 700 nm). The ruled width of the grating is to be 2 cm.a. Determine the minimum number of grooves required.b. If the diffraction pattern is focused by a 50-cm lens, what is the linear separation of a 1-Å interval in the vicinity of 500 nm? Get solution
11. A concave reflection grating of 2-m radius is ruled with 1000 grooves/mm. Light is incident at an angle of 30° to the central grating normal. Determine, for first-order operation, the (a) angular spread about the grating normal of the visible range of wavelengths (400 to 700 nm); (b) theoretical resolving power if the grating is ruled over a width of 10 cm; (c) plate factor in the vicinity of 550 nm; (d) radius of the Rowland circle in a Paschen-Runge mounting of the grating.Figure 1.... Get solution
12. How many grooves per centimeter are required for a 2-m radius, concave grating that is to have a plate factor of around 2 nm/mm in first order? Get solution
13. A plane reflection grating with 300 grooves/mm is blazed at 10°.a. At what wavelength in first order does the grating direct the maximum energy when used with the incident light normal to the groove faces?b. What is the plate factor in first order when the grating is used in a Czerny-Turner mounting with mirrors of 3.4-m radius of curvature? Get solution
14. A reflection grating, ruled over a 15-cm width, is to be blazed for use at 2000 Å in the vacuum ultraviolet. If its theoretical resolving power in first order is to be 300,000, determine the proper blaze angle for use (a) in a Littrow mount and (b) with normal incidence.Figure 1.... Get solution
15. Show that the spacing d of the fringes in the formation of a holographic grating, as shown in Figure 12-7c, is given by λ/(2 sin θ), where 2θ is the angle between the coherent beams. If the beams are argon-ion laser beams of wavelength 488 nm and the angle between beams is 120°, how many grooves per millimeter are formed in a plane emulsion (n = 1) oriented perpendicular to the fringes? What is the effect on the fringe separation d of an emulsion with a high refractive index? Get solution
16. A grating is needed that is able, working in first order, to resolve the red doublet produced by an electrical discharge in a mixture of hydrogen and deuterium: 1.8 Å at 6563 Å. The grating can be produced with a standard blaze at 6300 Å for use in a Littrow mount. Find (a) the total number of grooves required; (b) the number of grooves per millimeter on the grating with a blaze angle of 22°12′; (c) the minimum width of the grating. Get solution
17. An echelle grating is ruled over 12 cm of width with 8 grooves/mm and is blazed at 63°. Determine for a Littrow configuration (a) the range of orders in which the visible spectrum (400 to 700 nm) appears; (b) the total number of grooves; (c) the resolving power and minimum resolvable wavelength interval at 550 nm; (d) the dispersion at 550 nm; (e) the free spectral range, assuming the shortest wavelength present is 350 nm. Get solution
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