# HW-14s - SOLUTIONS 1 A diffraction grating has lines spaced...

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SOLUTIONS 1. A diffraction grating has lines spaced 2.00 m apart. Let's consider white visible light . (wavelengths ranging from 0.400 m for violet light to 0.700 m for red light) shining on . . it. (a) Determine all the angles for which interference maxima occur for violet light. sin 0.400 m 2.00 m 0.200 ) - . . œ 7 Î. œ 7Ð ÑÎÐ Ñ œ 7Ð Ñ 0 sin 0 7 œ Ê œ Ê œ ) ) 0 0 1 sin 0.200 11.5° 7 œ Ê œ Ê œ ) ) 1 0 2 sin 0.400 23.6° 7 œ Ê œ Ê œ ) ) 2 0 3 sin 0.600 36.9° 7 œ Ê œ Ê œ ) ) 3 0 4 sin 0.800 53.1° 7 œ Ê œ Ê œ ) ) 4 0 5 sin 1.000 90° 7 œ Ê œ Ê œ ) ) 5 0 (b) Determine all the angles for which interference maxima occur for red light. sin 0.700 m 2.00 m 0.350 ) - . . œ 7 Î. œ 7Ð ÑÎÐ Ñ œ 7Ð Ñ 0 sin 0 7 œ Ê œ Ê œ ) ) 0 0 1 sin 0.350 20.5° 7 œ Ê œ Ê œ ) ) 1 0 2 sin 0.700 44.4° 7 œ Ê œ Ê œ ) ) 2 0 3 sin 1.050 which is impossible 7 œ Ê œ ) 3 (c) Over what range of angles are the first, second, etc. orders of the spectrum found? First order: 11.5° to 20.5° Second order: 23.6° to 44.4° Third order (partial) begins at 36.9° Fourth order (partial) begins at 53.1° (d) Which orders are complete (i.e., have angles less than 90° for all wavelengths)?

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