Doublet Slit problem

  1. 1. The problem statement, all variables and given/known data
    A laser with wavelength d/8 is shining light on a double slit with slit separation 0.350 mm. This results in an interference pattern on a screen a distance L away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits.

    What is the wavelength lambda_2 of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.350 mm?


    2. Relevant equations
    location of interference maxima: dsin(theta) = m(lambda1)
    location of interference minima: dsin(theta) = (m+.5)(lambda2)


    3. The attempt at a solution

    i know that sin(theta) has to be the same for both of them, so i set these equations equal to sin(theta):
    sin(theta) = (m*lambda1)/d
    sin(theta) = ((m +.5 )*lambda2)/d

    therefore:
    (m*lambda1)/d = ((m +.5 )*lambda2)/d

    d is given in the problem, so you know d for both sides. you also know that d/8 equals lambda one, so that can be solved. i have tried 2=m for lambda one because it is the second maxima and 3.5=m for lambda two (mastering physics told me to remember that the first minima is zero, not 1). i keep on getting the wrong answer though! please help!!
     
  2. jcsd
  3. rl.bhat

    rl.bhat 4,433
    Homework Helper

    What is the wavelength lambda_2 of the second laser that would place its
    second maximum at the same location as the fourth minimum of the first laser, if d = 0.350 mm?
    So the equation should be
    2/d*d/x = 3.5/d*d/8 .Solve for x, and then find the wavelength.
     
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