PHY3 - Howard(clh2528 homework#3 shubeita(57885 This...

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Howard (clh2528) – homework #3 – shubeita – (57885) 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(part1of2)10.0points Two slits are illuminated by a 551 nm light. The angle between the zeroth-order bright band at the center of the screen and the fourth-order bright band is 18 . 2 . If the screen is 155 cm from the double-slit, how far apart is this bright band from the central peak? Correct answer: 50 . 9614 cm. Explanation: BasicConcept: y = L tan θ. Solution: y = L tan θ = (155 cm) tan(18 . 2 ) = 50 . 9614 cm . 002(part2of2)10.0points What is the distance between the two slits? Correct answer: 0 . 00705653 mm. Explanation: BasicConcept: d sin θ = Solution: The fourth-order bright band oc- curs when m = 4; therefore, d = m λ sin θ = 4 (551 nm) sin(18 . 2 ) = 0 . 00705653 mm . 003 10.0points A light source emits visible light of two wave- lengths, 459 nm and 481 nm. The light im- pinges upon a double slit apparatus, schemat- ically shown below. y 6 1 . 54 m 25 . 3 μ m S 1 S 2 θ viewing screen Find the separation between the sixth- order bright fringes. Correct answer: 0 . 803478 cm. Explanation: Let : L = 1 . 54 m , d = 25 . 3 μ m , and m = 6 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 Using the equation y bright = m λ L d , with m = 6, we find that the values of the fringe positions corresponding to these two wavelengths are y (1) 3 = m λ 1 L d = (6) (4 . 59 × 10 7 m) (1 . 54 m) (2 . 53 × 10 5 m) = 0 . 167635 m , y (2) 3 = m λ 2 L d
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Howard (clh2528) – homework #3 – shubeita – (57885) 2 = (6) (4 . 81 × 10 7 m) (1 . 54 m) (2 . 53 × 10 5 m) = 0 . 17567 m . Thus the separation between the two fringes is Δ y = y (2) 3 - y (1) 3 = (0 . 17567 m) - (0 . 167635 m) = 0 . 00803478 m = 0 . 803478 cm . 004 10.0points Consider the interference pattern on the screen formed by a 3-slit system, in which δ is the path difference between adjacent rays and φ is the corresponding phase angle differ- ence.
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