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Index of refraction when total internal reflection ceases

  1. Jul 14, 2007 #1
    light refractions problem

    I dont even know where to start with this problem. Can someone please help me out?
    As shown in Figure P22.49, a light ray is incident normal to on one face of a 30°-60°-90° block of zircon(n= 1.923) that is immersed in water.


    [​IMG]
    Figure P22.49
    (a) Determine the exit angle 4 of the ray.
    4 = wrong check mark°
    (b) A substance is dissolved in the water to increase the index of refraction. At what value of n2 does total internal reflection cease at point P?
    n2 =
     
  2. jcsd
  3. Jul 14, 2007 #2

    bel

    User Avatar

    For (a) : The light beam obviously entered at a normal to the shortest side of the triangular block since there wasn't any refraction, so using the fact that a triangle in a plane has a sum of internal angles of one hundred and eighty degrees, [tex]\theta_1=60^\circ [/tex]. And I suppose you know that in one single medium, for a reflection, incident angle equals reflected angle, using this, and Snell's law and the sum of internal angles for a triangle, you should be able to figure this out. Hope this helped.

    For (b) : Total internal reflection occurs if critical angle is smaller than incident angle. Using Snell's law, the critical angle is the arcsine of [tex]\frac{n_2}{n_1}[/tex].
     
    Last edited: Jul 14, 2007
  4. Jul 14, 2007 #3
    so using the sum of internal angles it looks like theta 3 would be 30 degrees? Because if you split the reflected ray there is a 30-60-90 triangle?
     
  5. Jul 15, 2007 #4
    1. The problem statement, all variables and given/known dataAs shown in Figure P22.49, a light ray is incident normal to on one face of a 30°-60°-90° block of zircon that is immersed in water.
    [​IMG]
    (b) A substance is dissolved in the water to increase the index of refraction. At what value of n2 does total internal reflection cease at point P?


    2. Relevant equations
    theta critical= arcsin(n2/n1) and total internal reflection ceases when theta critical is less than theta incident


    3. The attempt at a solution
    theta 4 is 46.16. I used 59.9=arcsin(n2/1.333) and got n2=1.15 but thats not correct but i dont understand because that is when theta critical is less than theta incident. theta incident is 60
     
  6. Jul 16, 2007 #5

    andrevdh

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    Homework Helper

    You need to consider total internal reflection at point P (at [tex]\theta _1[/tex]).

    Also n1 is for zirconium.
     
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