a) A double-slit experiment is set up using red light (l = 719 nm). A first orde

Question

a) A double-slit experiment is set up using red light (l = 719 nm). A first order bright fringe is seen at a given location on a screen. What wavelength of visible light (between 380 nm and 750 nm) would produce a dark fringe at the identical location on the screen?
(b) A new experiment is created with the screen at a distance of 1.9 m from the slits (with spacing 0.1 mm). What is the distance between the second order bright fringe of light with l = 691 nm and the third order bright fringe of light with l = 402 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)

Explanation / Answer

condition for constructive interference ( bright fringe ) is        ym = mD/d      ................. (1)    where, wavelength of the red light = 719 nm for first order bright fringe m = 1,           y1 = (1)D/d           y1 = (719 nm)D/d    .............. (2) condition for destructive interference ( dark fringe ) is         ym = (m + 1/2)D/d     ................. (3) Now to get the dark fringes at the same location we should have      (719 nm)D/d = (m + 1/2)D/d          (719 nm) = (m + 1/2)       ............. (4)    where, m = 0, 1 , 2 ,....... at , m = 1       (1 + 1/2) = (719 nm)      wavelength = 479.33 nm Therefore wavelength of visible light (between 380 nm and 750 nm) would produce a dark fringe at the identical location on thescreen is 479.33 nm. ................................................................................. first wavelength 1 = 691 nm = 691*10-9 m second wavelength 2 = 402 nm = 402*10-9 m distance between slits and screen D = 1.9 m slits separation d = 0.1*10-3 m for second order bright (m = 2) for first wave length ,                  y2 = 21D/d      ........... (5)    for third order bright (m = 3) for first wave length ,                  y3 = 32D/d      ........... (6) therefore ,         y2 - y3 = (21 - 32)D/d   ............ (7) substitute the given data in above equation , we get      y2 - y3 = (2*691*10-9 - 3*402*10-9)(1.9) / (0.1*10-3)                 = 3.344*10-3 m                 = 3.344 mm             ................................................................................. first wavelength 1 = 691 nm = 691*10-9 m second wavelength 2 = 402 nm = 402*10-9 m distance between slits and screen D = 1.9 m slits separation d = 0.1*10-3 m second wavelength 2 = 402 nm = 402*10-9 m distance between slits and screen D = 1.9 m slits separation d = 0.1*10-3 m for second order bright (m = 2) for first wave length ,                  y2 = 21D/d      ........... (5)    for third order bright (m = 3) for first wave length ,                  y3 = 32D/d      ........... (6) therefore ,         y2 - y3 = (21 - 32)D/d   ............ (7) substitute the given data in above equation , we get      y2 - y3 = (2*691*10-9 - 3*402*10-9)(1.9) / (0.1*10-3)                 = 3.344*10-3 m                 = 3.344 mm             for third order bright (m = 3) for first wave length ,                  y3 = 32D/d      ........... (6) therefore ,         y2 - y3 = (21 - 32)D/d   ............ (7) substitute the given data in above equation , we get      y2 - y3 = (2*691*10-9 - 3*402*10-9)(1.9) / (0.1*10-3)                 = 3.344*10-3 m                 = 3.344 mm            

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