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Midterm 1 Solutions - Version 019 Midterm 01 Yao(57045 This...

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Version 019 – Midterm 01 – Yao – (57045) 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 Light strikes the surface of a prism, n = 1 . 61, as shown in the figure. 45 If the prism is surrounded by a fluid, what is the maximum index of refraction of the fluid that will still cause total internal reflection within the prism? 1. 1.13844 2. 1.26572 3. 1.28693 4. 1.25158 5. 1.18087 6. 1.11016 7. 1.16673 8. 1.31522 9. 1.06773 10. 1.33643 Correct answer: 1 . 13844. Explanation: Basic Concept: sin θ c = n r n i Given: n i = 1 . 61 θ c = 45 Solution: sin θ c = n r n i n r = n i (sin θ c ) = 1 . 61 (sin 45 ) = 1 . 13844 002 10.0 points Hint: Use a small angle approximation; e.g. , sin θ tan θ θ and cos θ 1 . Consider the setup of double-slit experiment in the schematic drawing below. Note: As can be seen in the figure below, one of the double-slit interference maxima is located at the first single-slit diffraction minimum. a d y L S 1 S 2 θ viewing screen Determine the ratio d a ; i.e. , the slit separa- tion d compared to the slit width a . 1. d a = 9 2 2. d a = 7 2 3. d a = 5 4. d a = 3 2 5. d a = 3 correct 6. d a = 1 7. d a = 11 2 8. d a = 2
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Version 019 – Midterm 01 – Yao – (57045) 2 9. d a = 4 10. d a = 5 2 Explanation: At y there is a minimum for single-slit diffraction and a maxima for double-slit in- terference, as noted in the question . The first minimum for single-slit diffraction occurs when sin θ = λ a , (1) and the maxima for double-slit interference occur when sin θ = ( m ) λ d . (2) The first diffraction minimum for single-slit diffraction and the third double-slit interfer- ence maximum ( m = 3) occur at the same position y , as seen in the figure below. m 0 3 Figure: The dashed curve on the left of the screen is due to single slit interference. The dashed curve on the right of the screen is due to double slit interference. The screen position is zero amplitude and the positive direction is reflected on ei- ther side of the screen.
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