Question

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: 14 = 750 nm; 12 = 700 nm; 13 = 650 nm 14 = 600 nm; As = 560 nm; 16 = 500 nm; and Az = 450 nm. (b) Which colors, if any, overlap (i.e., are located at the same position) in the third order and fourth order diffractions? (a) 03 = 87°, 04 = 80°, 05 = 690, 0g = 56.40, 07 = 44.4° (b) is in the third-order overlaps with ly in the fourth-order (a) ) = 639 04/09 060 05 50 - 450 (b) in the third-orderoverlaps with is in the fourth-order (a) 03 900,0 = 75 05690 0 = 56:49 0 = 41.89 (b) in the third-order overlaps within the fourth-order

Answer 1

Son using the formula asino = na since it is third order diffraction n=3 d sin o = 3x a Sino = 34 d 3 x l-i → x3 650 nm, 0 - 03 taking & sine = 3 × 650nm 2000nm Sint 3 X 65 o 2ooo 77.2° 600 nm o = Oy taking x= xy Sin Ou 3 X 6oonm 200 o nom 04 = 64.207 taking x = 15 = 560 nm 3 x 5 6 ohm 05 Sin 05 2000 nm 57.1 5oo nm taking x = xo Sin Oo = 3 x 5oonm 2000nm = 48.6

taking x= x= 450, 0 = 0 Sin er 3 X 450nm 20oonm 42.5 for fourth order jen=4 l = 450 Sin Oz = 4x450nm 200onm - 64.2 as we can see this is equal to 3rd Order of Ay the correct option is the value with La> 0 = 77.2 Ou = 64.2 Os = 57.1 0 6 = 48.6 07 = 42.5 <b> Ay in the third order overlaps with X7 in fourth oxeler.