Question

The to most prominent wavelength in the light emitted by a hydrogen discharge lamp are 656 run (red) and 406 (blue). Light from a hydrogen lamp illuminates a diffraction grating with 500 lines/mm, and the light it observed on a screen 1.5 m behind the grading. What is the distance between the first - order read and blue fringes?

Answer 1

Condition for diffraction d sin theta = m lambda theta = sin^-1 (m lambda/d) d = 1/500 lines/mm = 2 times 10^-6 m theta_red = sin^-1 ((1) 656 times 10^-9/2 times 10^-6) = 19.1474 degree y_red = 1 tan theta_red = (1.5) tan (19.1474) = 0.520 m theta_blue = sin^-1 ((1) 486 times 10^-9/2 times 10^-6) = 14.063670 degree y_blue = (1.5) tan (14.063670) = 0.375 m delta_y = y_red - y_blue = 0.145 m