Two parallel slits are illuminated by light composed of twowavelengths, one of w

Question

Two parallel slits are illuminated by light composed of twowavelengths, one of which is 645 nm. On aviewing screen, the light whose wavelength is known produces itssecond dark fringe at the same place wherethe light whose wavelength is unknown produces its ninth-order bright fringe. The fringes are countedrelative to the central or zeroth-order bright fringe. What is theunknown wavelength? I thought the answer would be 179.17 becuase I did (m dark +.5)()/(m bright). But this isn't my answer. Any hint on whatIm doing wrong? Thanks Two parallel slits are illuminated by light composed of twowavelengths, one of which is 645 nm. On aviewing screen, the light whose wavelength is known produces itssecond dark fringe at the same place wherethe light whose wavelength is unknown produces its ninth-order bright fringe. The fringes are countedrelative to the central or zeroth-order bright fringe. What is theunknown wavelength? I thought the answer would be 179.17 becuase I did (m dark +.5)()/(m bright). But this isn't my answer. Any hint on whatIm doing wrong? Thanks

Explanation / Answer

Given :    We know that the condition when the dark fringeare formed is       d sin = ( m + 1/2 )        sin = ( m + 1/2 ) / 2    m = 2    Wavelength ( ) = 645 nm     sin = ( 2 + 1/2 ) / d            =( 5/2 ) 645 nm / d ------------ ( 1 )    Condition when the bright fringe are formed is dsin = m /      sin = ( m / d) /            = ( 9 / d ) /     --------- (2 )      Equating eqn ( 1 ) & ( 2 )     ( 5/2 ) 645 nm / d  =  ( 9 / d ) /              5 * 645 n m = 18 /         / = 5 * 645 nm / 18              = 180 nm I hope it helps you         / = 5 * 645 nm / 18              = 180 nm I hope it helps you

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