hw 41 - nguyen(jmn727 homework 41 Turner(59070 This...

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nguyen (jmn727) – homework 41 – Turner – (59070) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A helium-neon laser (wavelength 876 nm) is used to calibrate a diffraction grating. If the first-order maximum occurs at 17 . 7 , what is the line spacing? Correct answer: 2 . 88126 × 10 6 m. Explanation: We use the formula d sin θ = for m = 1, and obtain d = λ sin θ = 876 nm sin(17 . 7 ) = 876 nm 0 . 304033 = 2 . 88126 × 10 6 m . 002 (part 1 of 2) 10.0 points A diffraction grating is 5 . 41 cm long and con- tains 5670 lines per 2 . 65 cm interval. What is the resolving power of this grating in the third order? Correct answer: 34726 . 1. Explanation: Let : L = 5 . 41 cm , N = 5670 lines , and a = 2 . 65 cm . The diffraction grating’s line density is n = N a = (5670 lines) (2 . 65 cm) = 2139 . 62 lines / cm . Applying the formula for the resolving power R of the grating, R = N m = n L m , where m is the order of the diffraction, N = n L is the number of the illuminated lines of the diffraction grating, and L is the length of the diffraction grating, we obtain that for the third order ( m = 3) the resolving power R 3 of the grating is R 3 = n L m = (2139 . 62 lines / cm) (5 . 41 cm) (3) = 34726 . 1 . 003 (part 2 of 2) 10.0 points If two monochromatic waves incident on this grating have a mean wavelength of 510 nm, what is their wavelength separation if they are just resolved in the third order?
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