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MC (multiple choice) question about total internal reflection

  1. Aug 30, 2015 #1
    1. The problem statement, all variables and given/known data
    There is an optical fiber.A light ray enter it at i°.Total internal reflection occur at X.
    What are the necessary conditions for the light ray to travel along the core of the fiber?
    (I have cancelled B and D already.)
    A.n1>n2 and angle i should be greater than a certain value.
    C.n1>n2 and angle i should be less than a certain value.

    2. Relevant equations
    sinθa/sinθg=1/n; sinc=1/n;n1/n2=v1/v2

    3. The attempt at a solution
    For t.i.r. θ>c
    r=90°-θ
    r<90°-c
    But I don't understand how I can determine i is greater than or less than c(certain value) because i and r are not the same?
    Thank you so much!:)
    cainko
    (Sorry for my bad drawing)
     

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  2. jcsd
  3. Aug 30, 2015 #2

    berkeman

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    Staff: Mentor

    Welcome to the PF.

    What's an MC?
     
  4. Aug 30, 2015 #3

    TSny

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    Why do you say that n1 > n2? You might review your notes or textbook.

    In order for total internal reflection to occur at the boundary between n1 and n2, does the angle of incidence θ (in your drawing) need to be greater than the critical angle or less than the critical angle?

    What happens to the angle θ if the angle i is increased?
     
  5. Aug 30, 2015 #4
    MC is multiple choice question:)
     
  6. Aug 30, 2015 #5
    I am so sorry!!:( I draw the figure wrongly!
    for t.i.r. light must travel from low speed to high sped,for light ray:larger n --> smaller n ==>n1>n2

    θ will increase when angle i increased??
    sini/sinr = n ; sini increase-->sinr decrease==>θ=90°-r, r decrease θ increase?
    thx so much!
     

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  7. Aug 30, 2015 #6

    TSny

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    OK, no problem.
    sin(i)/sin(r) = n implies that sin(i) = n sin(r). So, if sin(i) increases what happens to sin(r)?
     
  8. Aug 30, 2015 #7
    decreases?
     
  9. Aug 30, 2015 #8

    TSny

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    The equation sin(i) = n sin(r) says that sin(i) and sin(r) are directly proportional to one another. If one increases so does the other.
     
  10. Aug 31, 2015 #9
    Oh, so r<90°-c ---> i is also<90°-c ?? so i is less than certain value?
     
  11. Aug 31, 2015 #10

    TSny

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    No. You are right that the condition r < 90 - c will produce total internal reflection at X.
    But that doesn't imply that the angle i must also be less than 90 - c. You are very close to the answer.

    Let rc = 90 - c. So, when r = rc, θ = c. You correctly stated that whenever r is less than rc, you will get total internal reflection at X.

    When r = rc, the angle i will have some value which we can call ic. How could you find ic if you knew rc? Does ic equal rc?

    What is the condition on angle i such that you get total internal reflection at X?
     
  12. Sep 4, 2015 #11
    as i increase when r increase, to make r< rc , i should be<ic too?
     
  13. Sep 4, 2015 #12

    TSny

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    Yes.
     
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