Light-path length difference

  1. 1. The problem statement, all variables and given/known data
    Two narrow slits are 0.12 mm apart. Light of wavelength 550 nm illuminates the slits, causing an interference pattern on a screen 1.0 m away. Light from each slit travels to the m=1 maximum on the right side of the central maximum.

    Part A -
    How much farther did the light from the left slit travel than the light from the right slit?
    Express your answer using two significant figures.
    2. Relevant equations
    r=dsin(theta)
    (theta)m = m*(lambda/d)
    y=L*tan(theta)

    ym = (m*lambda*L)/d

    3. The attempt at a solution

    I don't understand how to do these problems...

    thetam = (m*lambda*)/d
    thetam = (1*(5.5*10^-7m)/(1m)
    thetam = 5.5*10^-7


    path length difference = dsin(theta)
    so...
    r = d*sin(theta)
    r = 1m *sin(5.5*10^-7)
    r = 9.599^-9m
    r = 9.6nm
    That doesn't appear to be the correct answer(Unless MasteringPhysics is wrong). Sadly, I don't know if I did the right steps or used the correct equations.

    Any help is appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. alphysicist

    alphysicist 2,248
    Homework Helper

    Hi Foxhound101,


    Remember that this is really:

    [tex]
    \sin\theta=\frac{m\lambda}{d}
    [/tex]

    The approximation you are using ([itex]\theta=\frac{m\lambda}{d}[/itex]) is fine since the angle is small enough, but remember that this approximation is true if the angle is measured in radians. So the angle you found is [itex]5.5\times 10^{-7}\mbox{ rad}[/itex].

    This number was calculated with the angle measure set to degrees, not radians.
     
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