1. Show that when the incident ...-field is parallel to the plane of incidence, γ1 has the form given in Eq. (22-37). Get solution
2. A transparent film is deposited on glass of refractive index 1.50.a. Determine values of film thickness and (hypothetical) refractive index that will produce a nonreflecting film for normally incident light of 500 nm.b. What reflectance does the structure have for incident light of 550 nm? Get solution
3. Show from Eq. (22-42) that the normal reflectance of a single half-wave thick layer deposited on a substrate is the same as the reflectance from the uncoated substrate. ... Get solution
4. A single layer of SiO2 (n = 1.46) is deposited to a thickness of 137 nm on a glass substrate (n = 1.52). Determine the normal reflectance for light of wavelength (a) 800 nm; (b) 600 nm; (c) 400 nm. Verify the reasonableness of your results by comparison with Figure 22-2. Get solution
5. A 596-Å-thick layer of ZnS (n = 2.35) is deposited on glass (n = 1.52). Calculate the normal reflectance of 560 nm light. Get solution
6. Determine the theoretical refractive index and thickness of a single film layer deposited on germanium (n = 4.0) such that normal reflectance is zero at a wavelength of 2 μm. What actual material could be used? Get solution
7. A double layer of quarter-wave layers of Al2O3 (n = 1.60) and cryolite (n = 1.30) are deposited in turn on a glass substrate (n = 1.52).a. Determine the thickness of the layers and the normal reflectance for light of 550 nm.b. What is the reflectance if the layers are reversed? Get solution
8. Quarter-wave thin films of ZnS (n = 2.2) and MgF2 (n = 1.35) are deposited in turn on a substrate of silicon (n = 3.3) to produce minimum reflectance at 2 μm.a. Determine the actual thickness of the layers.b. By what percentage difference does the ratio of the film indices differ from the ideal?c. What is the normal reflectance produced? Get solution
9. By working with the appropriate transfer matrix, show that a quarter-wave/half-wave double layer, as in Figure 22-5, produces the same reflectance as the quarter-wave layer alone. Get solution
10. Write a computer program that will calculate and/or plot reflectance values for a double layer under normal incidence. Let input parameters include thickness and indices of the layers and the index of the substrate. Check results against Figure 22-4. Get solution
11. Prove the condition given by Eq. (22-47) for zero reflectance of three-layer, quarter-quarter-quarter-wave films when used with normal incidence. Do this by determining the composite transfer matrix for the three quarter layers and using the matrix elements in the calculation of the reflection coefficient in Eq. (22-36). Get solution
12. Using the materials given in Table 22-1, design a three- layer multifilm of quarter-wave thicknesses on a substrate of germanium that will give nearly zero reflectance for normal incidence of 2 μm radiation. Get solution
13. Determine the maximum reflectance in the center of the visible spectrum for a high-reflectance stack of high-low index double layers formed using nL = 1.38 and nH = 2.6 on a substrate of index 1.52. The layers are of equal optical thickness, corresponding to a quarter-wavelength for light of average wavelength 550 nm. The high-index material is encountered first by the incident light, as in Figure 22-8. Assume normal incidence and stacks of (a) 2; (b) 4; (c) 8 double layers. Get solution
14. A high-reflectance stack of alternating high-low index layers is produced to operate at 2 μm in the near infrared. A stack of four double layers is made of layers of germanium (n = 4.0) and MgF2 (n = 1.35), each of 0.5-μm optical thickness. Assume a substrate index of 1.50 and normal incidence. What reflectance is produced at 2 μm? Get solution
15. What theoretical ratio of high-to-low refractive indices is needed to give at least 90% reflectance in a high-reflectance stack of two double layers of quarter-wave layers at normal incidence? Assume a substrate of index 1.52. Get solution
16. Show that Rmax in Eq. (22-53) approaches 1 when either N approaches infinity or when the ratio nL/nH approaches zero. ... Get solution
2. A transparent film is deposited on glass of refractive index 1.50.a. Determine values of film thickness and (hypothetical) refractive index that will produce a nonreflecting film for normally incident light of 500 nm.b. What reflectance does the structure have for incident light of 550 nm? Get solution
3. Show from Eq. (22-42) that the normal reflectance of a single half-wave thick layer deposited on a substrate is the same as the reflectance from the uncoated substrate. ... Get solution
4. A single layer of SiO2 (n = 1.46) is deposited to a thickness of 137 nm on a glass substrate (n = 1.52). Determine the normal reflectance for light of wavelength (a) 800 nm; (b) 600 nm; (c) 400 nm. Verify the reasonableness of your results by comparison with Figure 22-2. Get solution
5. A 596-Å-thick layer of ZnS (n = 2.35) is deposited on glass (n = 1.52). Calculate the normal reflectance of 560 nm light. Get solution
6. Determine the theoretical refractive index and thickness of a single film layer deposited on germanium (n = 4.0) such that normal reflectance is zero at a wavelength of 2 μm. What actual material could be used? Get solution
7. A double layer of quarter-wave layers of Al2O3 (n = 1.60) and cryolite (n = 1.30) are deposited in turn on a glass substrate (n = 1.52).a. Determine the thickness of the layers and the normal reflectance for light of 550 nm.b. What is the reflectance if the layers are reversed? Get solution
8. Quarter-wave thin films of ZnS (n = 2.2) and MgF2 (n = 1.35) are deposited in turn on a substrate of silicon (n = 3.3) to produce minimum reflectance at 2 μm.a. Determine the actual thickness of the layers.b. By what percentage difference does the ratio of the film indices differ from the ideal?c. What is the normal reflectance produced? Get solution
9. By working with the appropriate transfer matrix, show that a quarter-wave/half-wave double layer, as in Figure 22-5, produces the same reflectance as the quarter-wave layer alone. Get solution
10. Write a computer program that will calculate and/or plot reflectance values for a double layer under normal incidence. Let input parameters include thickness and indices of the layers and the index of the substrate. Check results against Figure 22-4. Get solution
11. Prove the condition given by Eq. (22-47) for zero reflectance of three-layer, quarter-quarter-quarter-wave films when used with normal incidence. Do this by determining the composite transfer matrix for the three quarter layers and using the matrix elements in the calculation of the reflection coefficient in Eq. (22-36). Get solution
12. Using the materials given in Table 22-1, design a three- layer multifilm of quarter-wave thicknesses on a substrate of germanium that will give nearly zero reflectance for normal incidence of 2 μm radiation. Get solution
13. Determine the maximum reflectance in the center of the visible spectrum for a high-reflectance stack of high-low index double layers formed using nL = 1.38 and nH = 2.6 on a substrate of index 1.52. The layers are of equal optical thickness, corresponding to a quarter-wavelength for light of average wavelength 550 nm. The high-index material is encountered first by the incident light, as in Figure 22-8. Assume normal incidence and stacks of (a) 2; (b) 4; (c) 8 double layers. Get solution
14. A high-reflectance stack of alternating high-low index layers is produced to operate at 2 μm in the near infrared. A stack of four double layers is made of layers of germanium (n = 4.0) and MgF2 (n = 1.35), each of 0.5-μm optical thickness. Assume a substrate index of 1.50 and normal incidence. What reflectance is produced at 2 μm? Get solution
15. What theoretical ratio of high-to-low refractive indices is needed to give at least 90% reflectance in a high-reflectance stack of two double layers of quarter-wave layers at normal incidence? Assume a substrate of index 1.52. Get solution
16. Show that Rmax in Eq. (22-53) approaches 1 when either N approaches infinity or when the ratio nL/nH approaches zero. ... Get solution
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