Phys14 - 1 Unit 14 Physical Properties of Waves III 14.1...

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Unformatted text preview: 1 Unit 14 Physical Properties of Waves III 14.1 Superposition revisit 14.2 Young’s double-slit experiment 14.3 Phase change due to reflection 14.4 Diffraction 14.5 Resolving power 14.1 Superposition Revisit The simple addition of two or more waves to give a resultant wave is referred to as superposition. When waves are superposed, the result may be a wave of greater amplitude (constructive interference) or of reduced amplitude (destructive interference). 2 Constructive interference occurs: λ m l l = − 1 2 , where .... , 3 , 2 , 1 , ± ± ± = m Destructive interference occurs: λ ) 2 1 ( 1 2 − = − m l l , where .... , 3 , 2 , 1 , ± ± ± = m The source waves that we often used: • Monochromatic light : it consists of waves with a single frequency and hence a single color. • Coherent/incoherent light : Light waves that maintain a constant phase relationship with one another are referred to as coherent. Light waves in which the relative phases vary randomly with time are said to be incoherent. Example Two friends tune their radios to the same frequency and pick up a signal transmitted simultaneously by a pair of antennas. The friend who is equidistant from the antennas, at P , receives a strong signal. The friend at point Q 1 receives a very weak signal. Find the wavelength of the radio waves if d = 7.50 km, L = 14.0 km, and y = 1.88 km. Assume that Q 1 is the first point of minimum signal as one moves away from P in the y direction. Answer: The first minimum in the y direction from the maximum at point P , we know that the path difference, l 2 – l 1 , is half a wavelength. The path length l 1 : km km km km y d L l 1 . 14 88 . 1 2 ) 50 . 7 ( ) . 14 ( 2 2 2 2 2 1 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + = The path length l 2 : km km km km y d L l 1 . 15 88 . 1 2 ) 50 . 7 ( ) . 14 ( 2 2 2 2 2 2 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + = By the relation 2 1 2 λ = − l l , it gives km . 2 = λ . This wavelength corresponds to a frequency of about 150 kHz. 3 14.2 Young’s double-slit experiment Monochromatic light from a narrow vertical slit S falls on two other narrow slits S 1 and S 2 which are very close together and parallel to S . S 1 and S 2 act as two coherent sources (both being derived from S ) and if they (as well as S ) are narrow enough, diffraction causes the emerging beams to spread into the region beyond the slits. Superposition occurs in the shaded area where the diffracted beams overlap. Alternate bright and dark equally-spaced vertical bands (interference fringes) can be observed on a screen. Note that if either S 1 or S 2 is covered the bands disappear. An expression for the separation of two bright (or dark) fringes can be obtained as follows....
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This note was uploaded on 09/06/2010 for the course BSC PHY1417 taught by Professor Prof during the Spring '08 term at HKU.

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Phys14 - 1 Unit 14 Physical Properties of Waves III 14.1...

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