Our old high school friend is confused again. She asks, \"OK, I getthat all of t

Question

Our old high school friend is confused again. She asks, "OK, I getthat all of this interference and diffraction pattern stuff shoulddepend on the path difference. After all, that's what's differentabout a given spot on the viewing screen: different light beamsmust travel different distances to get there. What I don't get ishow the wavelength of the light makes any difference at all. Why doyou get different light and dark spot separations for differentcolors of light in the same apparatus?"

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Explanation / Answer

the positions of the first minima measured from the centralaxis is y = L * sindark the general condition for destructive interference is sindark = m * (/a) m =±1,±2,3,............. or y = L * m * (/a) -----------(1) L is the distance between the slits and the screen,m is theorder of diffraction, is the wavelength of the light and a isthe width of the slits. In equation (1) L,m and a are constant for the apparatus andtherefore the value of y depends only on the wavelength of lightand as the wavelength is different for different colors thereforewe get different light and dark spot separations for differentcolors of light in the same apparatus. the general condition for destructive interference is sindark = m * (/a) m =±1,±2,3,............. or y = L * m * (/a) -----------(1) L is the distance between the slits and the screen,m is theorder of diffraction, is the wavelength of the light and a isthe width of the slits. In equation (1) L,m and a are constant for the apparatus andtherefore the value of y depends only on the wavelength of lightand as the wavelength is different for different colors thereforewe get different light and dark spot separations for differentcolors of light in the same apparatus.

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