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Homework Help: Optics Problem - light passing through 3 mediums

  1. Feb 24, 2010 #1
    1. Light propagating from water into air is incident on the water surface at the angle of total internal reflection. (a-int = 48.75 degrees) A plane parallel glass plate (n-glass = 1.5) is brought into contact with the surface of the water. Calculate the angle 'alpha-external' (a-ext for notation simplicity) between the top surface of the glass plate and the direction at which the light will emerge from the glass plate.

    n-air = 1
    n-water = 1.33
    n-glass = 1.5

    2. (n-water)(sin(Theta-water)) = (n-glass)(sin(theta-glass)), (n-glass)(sin(theta-glass)) = (n-air)(sin(theta-air))

    3. I have combined the two equations to get:

    sin(theta-air) = (n-air/n-water)sin(a-int)

    where by not needing to take into account the refractive index n-glass. this gives me a value of:

    (theta-air) = 48.75, so 90-(theta-air) = a-ext = 41.25

    I have then made the calculations separately for each barrier and came out with a value of 1.1 for a-ext? Could anyone verify if either of these solutions are correct?

    The question then goes on to ask what happens if (n-glass) = 1.2, 1.4 and 2. So i presume i must take into consideration the glass block overall, and my first attempt at combining the 2 snell equations is incorrect.
  2. jcsd
  3. Feb 25, 2010 #2


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    2. (n-water)(sin(Theta-water)) = (n-glass)(sin(theta-glass)), (n-glass)(sin(theta-glass)) = (n-air)(sin(theta-air))
    This formula is correct.
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