Question

1. A diffraction grating is used to separate the spectral lines of light, emanating from a gas discharge tube (e.g., a neon light), that is normally incident on the grating. On a screen placed 2.0 m from the grating, the third-order (m = 3) interference maximum for violet light (λ = 4.4 × 10−7 m) is found to be 0.20 cm farther from the location of the central maximum (m = 0) on the screen than the second-order maximum of red light (λ = 6.5 × 10−7 m). (a) How far from the central maximum is the location of the second-order red light maximum? (Recall the small-angle approximation, tan θ ≈ sin θ.) (b) What must be the density of the slits, i.e., the number of lines ruled per centimeter, of the grating? (c) If the screen is 2.0-meters wide, with its center positioned at the location of the central maximum of the spectral light being analyzed, how many violet light interference maxima are visible on the screen? (Careful, can the small-angle approximation be used here?)  

Answer 1