# Chap 33 SM - Chapter 33 Interference and Diffraction...

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1059 Chapter 33 Interference and Diffraction Conceptual Problems 1 A phase difference due to path-length difference is observed for monochromatic visible light. Which phase difference requires the least (minimum) path length difference? ( a ) 90 o ( b ) 180 o ( c ) 270 o ( d ) the answer depends on the wavelength of the light. Determine the Concept The phase difference δ due to a path difference Δ r are related according to λ π r Δ = 2 . Therefore, the least path length difference corresponds to the smallest phase difference. ( ) a is correct. 2 Which of the following pairs of light sources are coherent: ( a ) two candles, ( b ) one point source and its image in a plane mirror, ( c ) two pinholes uniformly illuminated by the same point source, ( d ) two headlights of a car, ( e ) two images of a point source due to reflection from the front and back surfaces of a soap film. Determine the Concept Coherent sources have a constant phase difference. The pairs of light sources that satisfy this criterion are ( b ), ( c ), and ( e ). 3 [SSM] The spacing between Newton’s rings decreases rapidly as the diameter of the rings increases. Explain qualitatively why this occurs. Determine the Concept The thickness of the air space between the flat glass and the lens is approximately proportional to the square of d , the diameter of the ring. Consequently, the separation between adjacent rings is proportional to 1/ d . 4 If the angle of a wedge-shaped air film, such as that in Example 32-2 is too large, fringes are not observed. Why? Determine the Concept There are two possible reasons that fringes might not be observed. (1) The distance between adjacent fringes is so small that the fringes are not resolved by the eye. (2) Twice the thickness of the air space is greater than the coherence length of the light. If this is the case, fringes would be observed in the region close to the point where the thickness of the air space approaches zero. 5 Why must a film that is used to observe interference colors be thin? Determine the Concept Colors are observed when the light reflected off the front and back surfaces of the film interfere destructively for some wavelengths and

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Chapter 33 1060 constructively for other wavelengths. For this interference to occur, the phase difference between the light reflected off the front and back surfaces of the film must be constant. This means that twice the thickness of the film must be less than the coherence length of the light. The film is called a thin film if twice its thickness is less than the coherence length of the light. 6 A loop of wire is dipped in soapy water and held up so that the soap film is vertical. ( a ) Viewed by reflection with white light, the top of the film appears black. Explain why. ( b ) Below the black region are colored bands. Is the first band red or violet?
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Chap 33 SM - Chapter 33 Interference and Diffraction...

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