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Red and Violet Light through a Prism (Snell's Law)

  1. Mar 28, 2015 #1
    1. The problem statement, all variables and given/known data

    A ray of white light strikes the surface of a 4.0-cm-thick slab of flint glass (Θ1 = 60°). As the ray enters the glass, it is dispersed into its constituent colors.

    Estimate how far apart the rays of deepest red and deepest violet light are as they exit the bottom surface. Assume nred = 1.57 and nviolet = 1.60.

    Θ1 = 60°
    n1 = 1 (air)
    Θ2violet = ?
    Θ2red = ?
    nviolet = 1.60
    nred =1.57
    d (adj) = 4 cm
    Δx = ?

    2. Relevant equations

    Snell's Law: n1*sin(Θ1) = n2*sin(Θ2)
    tan(Θ) = opp/adj

    3. The attempt at a solution

    n1*sin(Θ1) = n2*sin(Θ2r)
    sin-1((sin 60°)/(1.57)) = Θ2r = 33.5°

    n1*sin(Θ1) = n2*sin(Θ2v)
    sin-1((sin 60°)/(1.60)) = Θ2v = 32.8°

    tan(Θ2r) = opp/adj
    dr = tan(33.5°) * 4 cm = 2.65 cm

    dv = tan(32.8°) * 4 cm = 2.58 cm

    Δx = 2.65 cm - 2.58 cm = 0.7 mm

    It says that this answer is not correct, but I am nearly 100% sure this is how it should be done!
     
  2. jcsd
  3. Mar 28, 2015 #2

    TSny

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    Your work looks correct to me. Since no picture is provided, it is important to know how the angle of 60o is measured. I assume it's the angle between the incoming light ray and the normal to the surface of the glass.
     
  4. Mar 28, 2015 #3
    Yeah, I'm really unsure of why it's marking me wrong. Here's the reference figure: http://i.imgur.com/5r2P1vY.jpg?1
     
  5. Mar 28, 2015 #4

    TSny

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    Ah. Note that the 60o shown in the figure is not the angle of incidence.
     
  6. Mar 28, 2015 #5
    Ah! Thank you so much! The correct answer came out to be 0.28 mm.
     
  7. Mar 28, 2015 #6
  8. Mar 28, 2015 #7

    TSny

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