1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Displacement of emerging light ray

  1. May 22, 2012 #1
    1. The problem statement, all variables and given/known data

    A light ray is incident on a flat piece of glass with index of refraction n. Show that if the incident angle θ is small, the emerging ray is displaced a distance d = tθ(n - 1)/n form the incident ray, where t is the thickness of the glass and θ is in radians.

    2. Relevant equations

    n1sinθ1 = n2sinθ2

    3. The attempt at a solution

    Using Snell's law, right triangles, sin(a-b) identity, and small angle approximation, I have got it to:

    d = tθ(n-(cosθ/cosθR))/n [θR is angle of refraction in glass]

    how do I get cosθ/cosθR = 1?
     
    Last edited: May 22, 2012
  2. jcsd
  3. May 22, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    You should be able to get to the result in a more direct way. What is your understanding of "the small angle approximation"?
     
  4. May 22, 2012 #3
    sin(theta) = theta for theta < .2 radians
     
  5. May 22, 2012 #4

    gneill

    User Avatar

    Staff: Mentor

    Yes, anything else? (Hint: Another trig function has almost the same value for small angles)
     
  6. May 22, 2012 #5
    oh, yeah, cos(theta) = 1 - theta/2
     
  7. May 22, 2012 #6
    I might use that back when I used the sin(A-B)=sinAcosB-sinBcosA identity.
     
  8. May 22, 2012 #7
    I'll try it from the start with this added info. thanks gneill.
     
  9. May 22, 2012 #8

    gneill

    User Avatar

    Staff: Mentor

    There's yet ANOTHER trig function that's ~θ when θ is small. You may find it even more convenient...
     
  10. May 22, 2012 #9
    OK, I got it solved! Thanks for the help, I'd never heard about small angle approximation for cos and tan until this problem. The tan approximation was the key piece I was missing.

    Thanks for the help!
     
  11. May 22, 2012 #10

    gneill

    User Avatar

    Staff: Mentor

    Glad to help :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Displacement of emerging light ray
  1. Ray of light (Replies: 1)

  2. Light rays (Replies: 1)

  3. OPD of 2 light ray (Replies: 3)

Loading...