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Math Help - Angle of refraction

  1. #1
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    Angle of refraction

    Hi
    I have this little problem bothering. The question goes like this:
    A ray enters an equilateral glass prism of refractive index 1.55 at the midpoint of one side of the prism at an angle of inceidence of 35 degrees.
    a. Sketch this arrangement and show that the angle of refraction of the light ray in the glass is 22 degrees.
    b. Show that the angle of incidence where the light ray leaves the glass prism is 38 degree.
    c. Calculate the angle of refraction of the light ray where it leaves the prism.


    2. Relevant equations
    n= Sin i/Sin r



    3. The attempt at a solution

    I am able to do a. For b this is my working:
    1.55=Sin i/Sin 22

    But I obtained 35.5 degrees. Can anyone please explain where I am going wrong?
    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by gbenguse78 View Post
    Hi
    I have this little problem bothering. The question goes like this:
    A ray enters an equilateral glass prism of refractive index 1.55 at the midpoint of one side of the prism at an angle of inceidence of 35 degrees.
    a. Sketch this arrangement and show that the angle of refraction of the light ray in the glass is 22 degrees.
    b. Show that the angle of incidence where the light ray leaves the glass prism is 38 degree.
    c. Calculate the angle of refraction of the light ray where it leaves the prism.


    2. Relevant equations
    n= Sin i/Sin r



    3. The attempt at a solution

    I am able to do a. For b this is my working:
    1.55=Sin i/Sin 22

    But I obtained 35.5 degrees. Can anyone please explain where I am going wrong?
    Thanks.
    The angle of incidence for part b is the angle where the internal ray hits the second face of the prism. This is pure geometry no further refraction is involved. Draw a picture, you will find that the second angle of incidence depend on the first angle of refraction and the geometry of the equilateral prism.

    CB
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  3. #3
    Member
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    Nov 2009
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    Thanks. I have got it now!
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