Question

Question 25 4 pts A diffraction grating has a diffraction grating constant d = 2000 nm. (a) Identify which of the following colors (wavelengths) can be observed in the third-order diffraction by calculating the angles at which they can be observed: 11 = 750 nm; 12 = 700 nm; 13 = 650 nm 14 = 600 nm; 15 = 560 nm; 16 = 500 nm; and 17 = 450 nm. (b) Which colors, if any, overlap (i.e., are located at the same position) in the third order and fourth order diffractions? O (a) 03 = 87°, 04 = 80°, 05 = 690, 06 = 56.4°, 07 = 44.4° (b) As in the third-order overlaps with 17 in the fourth-order O (a) 03 = 830.04 = 70°, 05 = 60°, 0. = 50°, 07 = 45° (b) X6 in the third-order overlaps with As in the fourth-order (a) 03 = 90°.04 - 750,05 690, 06 = 56.49, 07 = 41.8° (b) X4 in the third-order overlaps with in the fourth-order (a) 03 = 77.29, 04-64.2°, 05 = 57.1°, 0. = 48.6° 0 = 42.5° (b) 4 in the third-order overlaps with 7 in the fourth-order O (a) 63 - 67º. 04 = 530, 05-46°, 0. = 33.6°, 07-30.8° (b) X3 in the third-order overlaps with X6 in the fourth-order

Answer 1

Solution: in the direction o For the min order principal maximum We have the condition, (a+b) sine ma d sino grating Const. D OR, ma where Given, d 2.000 nm m as for a - 750 nm 2000 sino, 3 X 750 Sino, 1.125 . undefined . [-12 15 Sino, s 1 ] For 22 - 700 nm, 2000 Sindz - 3 x 700 Sino2 1:05 which is undefined. for ay = 650 nm, 2000 Sinag = 3 x 650 0.975 Sinoy = 3 X 600 og - 77. 2 for a = 600 nm, 2000 Sinoy = Sinoy = 0.9 = 04 = 64.2 for 15 = 560nm, 2000 Sin05 2 3 X 560 052 For 16 = 500 nm for a7 = 450nm 2.000 Sineo 3 x 500 42.5° 48.60 57.10 07 (b) 3 x au = 4X27 = 1800 (constant) ay in 3rd order and 27 in 4 th order. wiu Norlop