# Parenrightbigg ? where m 0 1 2 3 so for the third

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parenrightbigg λ , where m = 0 , ± 1 , ± 2 , ± 3 , so for the third dark fringe ( m = 2), δ = parenleftbigg m + 1 2 parenrightbigg λ = 5 2 λ and δ λ = φ 2 π = 5 2 φ = 5 π . 006(part2of2)10.0points Using the small angle approximation ( θ = sin θ = tan θ ) , if the distance from the central bright region to the third dark fringe is y , what is the wavelength of the light? 1. λ = 2 7 d y L 2. λ = 2 5 d L y 3. λ = 2 5 L y d 4. λ = 2 7 d L y 5. λ = 2 5 d y L correct 6. None of these 7. λ = 1 3 d y L 8. λ = 1 3 d L y 9. λ = 2 7 L y d 10. λ = 1 3 L y d Explanation:
scribner (eks662) – interference diffraction HW – yeazell – (55745) 3 r 2 r 1 y L d S 1 S 2 θ = tan 1 parenleftBig y L parenrightBig viewing screen δ d sin θ r 2 - r 1 P O negationslash S 2 Q S 1 90 Q r 2 r 1 d = h 2 S 1 S 2 θ = tan 1 parenleftBig y L parenrightBig θ δ 2 h sin θ r 2 - r 1 negationslash S 2 Q S 1 90 Q The angle θ from the slits’ midpoint to the y position on the screen is tan θ = y L sin θ , so the wavelength of the light for the third dark fringe ( m = 2) is parenleftbigg m + 1 2 parenrightbigg λ = d sin θ 5 2 λ = d y L λ = 2 5 d y L . 007 10.0points A screen is illuminated by light with wave length λ as shown. The distance from the slits to the screen is L . y L d S 1 S 2 θ viewing screen Using the small angle approximation ( θ = sin θ = tan θ ) , how far apart y is the sixth dark fringe from the central bright fringe? 1. y = 11 2 L d λ 2. y = 6 d λ L 3. y = 6 L d λ 4. y = 13 2 d λ L 5. y = 11 2 L λ d correct 6. y = 13 2 L d λ 7. y = 6 L λ d 8. y = 11 2 d λ L 9. y = 13 2 L λ d 10. None of these Explanation: For dark fringes δ = d sin θ = parenleftbigg m + 1 2 parenrightbigg λ , where m = 0 , ± 1 , ± 2 , ± 3 .
L y = 11 2 L λ d . 008 10.0points In a Young’s double-slit experiment using 294 nm light, a thin piece of plexiglass of refractive index 1 . 52 covers one of the slits. If the center point on the screen is a dark spot instead of a bright spot, what is the minimum thickness of the plexiglass?
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