HW #12-solutions

# HW #12-solutions - nanni(arn437 HW#12 Erskine(56905 1 This...

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Unformatted text preview: nanni (arn437) HW #12 Erskine (56905) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A screen is illuminated by monochromatic light as shown in the figure below. The distance from the slits to the screen is 6 . 4 m . 3 . 2cm 6 . 4 m . 56mm S 1 S 2 viewing screen What is the wave length if the distance from the central bright region to the seventh dark fringe is 3 . 2 cm . Correct answer: 430 . 764 nm. Explanation: Basic Concepts: For bright fringes, we have d sin = m , and for dark fringes, we have d sin = parenleftbigg m + 1 2 parenrightbigg , where m = 0 , 1 , 2 , 3 , . From geometry, we have y = L tan . Let : y = 3 . 2 cm = 0 . 032 m , L = 6 . 4 m , and d = 0 . 56 mm = 0 . 00056 m . r 2 r 1 y L d S 1 S 2 = ta n 1 parenleftBig y L parenrightBig viewing screen d sin r 2- r 1 P O negationslash S 2 Q S 1 90 Q r 2 r 1 d S 1 S 2 = ta n 1 parenleftBig y L parenrightBig d s i n r 2- r 1 negationslash S 2 Q S 1 9 Q Solution: The angle from the slits mid- point to the y position on the screen is = arctan bracketleftBig y L bracketrightBig = arctan bracketleftbigg (0 . 032 m) (6 . 4 m) bracketrightbigg = 0 . 00499996 rad . The wavelength of the light for the seventh dark fringe, m = 6, is = d sin parenleftbigg m + 1 2 parenrightbigg = (0 . 00056 m) sin(0 . 00499996 rad) (6 . 5) = 4 . 30764 10 7 m = 430 . 764 nm . 002 10.0 points Two coherent microwave sources that produce waves of wavelength 2 cm are in the xy plane, one on the y axis at y = 9 cm and the other at x = 3 cm, y = 8 cm. If the sources are in phase, find the differ- ence in phase between the two waves from these sources at the origin. Correct answer: 82 . 0793 . Explanation: nanni (arn437) HW #12 Erskine (56905) 2 Let : vectorx 1 = ( x 1 , y 1 ) = (0 , 9 cm) , vectorx 2 = ( x 2 , y 2 ) = (3 cm , 8 cm) , and = 2 cm . The path difference between the distances from these two sources to the origin is r = r 1- r 2 = radicalBig x 2 1 + y 2 1- radicalBig x 2 2 + y 2 2 = 9 cm- radicalBig (3 cm) 2 + (8 cm) 2 = 0 . 455996 cm , so the difference in phase is = r 360 = (0 . 455996 cm) (360 ) 2 cm = 82 . 0793 . 003 (part 1 of 3) 10.0 points Consider the setup of a four slit diffraction experiment shown in the figure. 4 3 2 1 y L Find the path difference difference between two rays from adjacent slits which gives rise to the first minimum. 1. = 2 3 2. = 1 4 correct 3. = 2 5 4. = 1 2 5. = 3 4 6. = 1 5 7. = 8. = 2 9. = 3 5 10. = 1 6 Explanation: Basic Concept: Light Interference E 1 E 2 E 3 E 4 The first minimum occurs when the four phasor vectors of the four rays in the phasor diagram form a closed square. Thus, the relative phase angle between the adjacent phasor vectors is given by...
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HW #12-solutions - nanni(arn437 HW#12 Erskine(56905 1 This...

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