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Homework #3-solutions - mehta(snm425 Homework 3...

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mehta (snm425) – Homework 3 – erskine – (58715) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Is diffraction more pronounced through a small or a large opening? 1. small correct 2. It depends on the frequency of the light. 3. large Explanation: Diffraction is more pronounced through a small opening. 002 10.0 points Consider the setup of a single slit experiment. y 3 L a S 1 S 2 θ viewing screen × 15 Find the height y 3 , where the third mini- mum occurs. Use a small angle approximation sin θ = tan θ . 1. y 3 = 5 λ L a 2. y 3 = 4 λ L a 3. y 3 = 9 2 λ L a 4. y 3 = 2 λ L a 5. y 3 = 3 λ L a correct 6. y 3 = 5 2 λ L a 7. y 3 = 7 2 λ L a 8. y 3 = 1 λ L a 9. y 3 = 11 2 λ L a 10. y 3 = 3 2 λ L a Explanation: The first minimum is at β = 2 π , where β = 2 φ = 2 π , where φ = π is the phase difference of the two rays for destructive interference. The third minimum occurs at β = 6 π , which corresponds to a path difference δ be- tween two end rays δ = β k = 6 π parenleftbigg 2 π λ parenrightbigg = 3 λ θ = δ a = y 3 L y 3 = δ a L = 3 λ L a , where k 2 π λ . 003 10.0 points Light from a He-Ne laser of wavelength 529 . 4 nm is incident on a single slit. What is the minimum width for which no diffraction minima are observed? Correct answer: 529 . 4 nm. Explanation: Given : λ = 529 . 4 nm . The first minimum is at a sin θ = λ . This equation has no solution if λ a > 1. Hence the minimum width of the single slit for which no diffraction minima are observed is a min = λ = 529 . 4 nm .
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mehta (snm425) – Homework 3 – erskine – (58715) 2 004 10.0 points A binary star system in the constellation Orion has an angular separation between the two stars of 4 . 89 × 10 6 rad. If the wavelength is 572 nm, what is the smallest diameter a telescope can have and just resolve the two stars? Correct answer: 0 . 142708 cm. Explanation: From the formula θ = 1 . 22 λ D , where D is the diameter of the telescope, we infer that the smallest diameter the telescope needs to resolve the two stars is D = 1 . 22 λ θ = 1 . 22 572 nm 4 . 89 × 10 6 rad = 0 . 00142708 m = 0 . 142708 cm . 005 10.0 points A good diffraction grating has 2590 lines / cm. What is the distance between two lines in the grating? Correct answer: 0 . 0003861 cm. Explanation: The distance between the lines is the recip- rocal of the given value. 006 (part 1 of 2) 10.0 points A spectrometer uses a grating with 12700 lines / cm. Find the angle at which red light, 631 . 8 nm, has the first-order bright band. Correct answer: 53 . 3586 . Explanation: Basic Concepts For diffraction gratings, λ = xd L = d sin θ = 1 n sin θ sin θ = θ = arcsin( ) Dimensional analysis of : 1 cm nm · 100 cm 1 m 1 m 10 9 nm = rad 007 (part 2 of 2) 10.0 points Find the angle at which blue light, 425 . 1 nm, has the first-order bright band. Correct answer: 32 . 6753 . Explanation: 008 10.0 points X-rays of wavelength 0 . 198 nm are reflected from a certain crystal, and the first-order maximum occurs at an angle of 7 . 8 .
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