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Wave Nature of Light - Calculating Wavelength (Double Slit Exp)

  1. Oct 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Monochromatic light falls on two very narrow slits 0.046 mm apart. Successive fringes on a screen 5.30 m away are 7.0 cm apart near the center of the pattern. Determine the wavelength of the light to two significant figures.

    2. Relevant equations

    x2 ≈ Lθ2 = L (2λ) / d

    3. The attempt at a solution

    I'm guessing the θ is very small so I can assume sin θ ≈ θ in radians. When the problem said the successive fringes were 7.0 cm apart near the center of the pattern, I thought that meant x2 was 7.0 cm above x1.

    λ = dx2 / 2L
    λ = (0.07 m)(4.6 *10^-5 m) / (2 * 5.30 m)
    λ = 3.01 * 10^-7 m
     
  2. jcsd
  3. Oct 21, 2012 #2

    mfb

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    I think there is a factor of 2 missing (or too much) somewhere. With the distance d between the slits, two adjacent fringes appear with an angle of ##\alpha \approx \frac{\lambda}{d}## between them.
    In addition: With twice your calculated wavelength, the light is visible.
     
  4. Oct 21, 2012 #3
    I multiplied my answer by "2" and got it correct but I am still unsure why I should have multiplied by "2." Were you stating at 3.01 * 10 ^-7 m light is not visible?
     
  5. Oct 22, 2012 #4

    mfb

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    That corresponds to 301nm - ultraviolet radiation.

    I think you divided by 2, where you shouldn't have done that.
     
  6. Oct 22, 2012 #5
    It looks like you picked up a wrong formula there. Take a look at 'Young's slits' in Wikipedia.
     
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