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Finding the incidence angle for refraction

  1. Apr 17, 2013 #1
    1. The problem statement, all variables and given/known data

    I am to find the angle of incidence of a light ray before it undergoes refraction. Light is refracted in the second medium at an angle of 76 degrees measured from the normal. The second index of refraction is 1.386. The index of refraction for the initial or first medium is 1.336.

    2. Relevant equations

    Snell's Law n1sin(theta 1) = n2 sin (theta 2)

    3. The attempt at a solution

    I worked through Snell's Law and found that sin ( theta one) is 1.006 . When I attempt to take the inverse SIN for the angle, I get domain error because the value is greater than 1.

    This can't be internal reflection because the second medium has a higher index of refraction than the first?

    All help is appreciated! Thanks
  2. jcsd
  3. Apr 17, 2013 #2


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    Although this is not total internal reflection, the situation here is related to the critical angle.

    If a ray of light refracts going from material 1 to material 2, then that ray should be "reversible". That is, light should be able to travel the same path in the reversed direction from material 2 back into material 1.

    So, for the reversed path in your problem, the ray would start in material 2 and have an angle of incidence of 76 degrees. How is 76 degrees related to the critical angle for going from material 2 to material 1?

    Another way to look at the problem is to consider the light going from material 1 into material 2 with greater and greater angles of incidence in material 1. As you increase the angle of incidence in material 1, what happens to the angle of refraction in material 2? What would you let the angle of incidence be to find the greatest possible angle of refraction in material 2? How does this maximum angle of refraction compare with 76 degrees?
  4. Apr 17, 2013 #3
    I noticed you left reversible in quotations. Why must we address a reversible ray when the ray is not physically going from a high medium to a lower medium of index?

    I can see what you're saying as the incidence angle is increased, I even did some online simulators, but I cannot grasp as to why this occurs. I thought this type of reflection only occurred again when going from a high index to a low index.
  5. Apr 17, 2013 #4


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    If a ray of light is possible in one direction, then the reversed ray must also be possible. (Both rays will satisfy Snell's law). See the attached picture. So, if you can show that the reversed ray is impossible, that means the original ray is impossible. That's why you can't get an answer with your calculator.
    We're not talking about reflection here, just refraction in going from medium 1 to medium 2. There is a greatest value that θ2 can be. If 76o is greater than that maximum possible angle of refraction, then it's impossible for a ray to be refracted at 76o. So, that's another way to see why your calculator is giving an error.

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