Question

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Problem 8: When yellow sodium light, X = 600 nm falls on a diffraction grating, its first-order peak (m = 1) on a screen 40.0 cm away falls 1.2 cm from the central peak. You may use the small angle approximation sino tan for both parts of this problem. (a) How many lines/cm are on the diffraction grating? Answer: 500 lines/cm. (b) When another source of light is passed through this diffraction grating, its first-order peak (m = 1) on the screen, 40.0 cm away, falls 1.4 cm from the central peak. What is the wavelength of this source in nm? Answer: 700 nm.

Answer 1

(a) The angle of first order from distance is, tan 0, = 1 tan L 1.2 40 1.2 0 = tan 40 =1.72° The expression from young's double slit is, d sin = m2 d sin 1.72° = (1.0)(600x10-°) d(0.0299865)=(600x10- 600x10° d= 0.0299865 = 2.0x10 m The number of lines per cm in the grating is, 1 1 d 2.0x10-5 = 4.9977x104 = 50000 line/cm (b) The angle of first order from distance is, vi tan L 1.2 tan 40 1.4 40 = 2.0° The expression from young's double slit is, d sin = ma d sin 2.0° = (1.0)(600x10°) d(0.03497858)= (600x109) 600 x 10 d = 0.03497858 = 1.72x10- m = tan-

The new wave length is, d sin = m2 (1.72x10-*)sin 2.0° = (1.0) 2 1 = (1.72x10- sin 2.0° = 600.27xx 10-ºm =600.27 nm