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Thread: Ray tracing a thin prism

  1. #1 Ray tracing a thin prism 
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    I finally found something about thin prisms on the web
    a thin prism, which is generally a prism with an apical angle of less than 15°. For simplicity, we will assume that the initial object ray is striking the first surface normally (or perpendicularly). Since the ray is normal—or at a 90° angle—to the first surface, no refraction occurs. However, once the ray strikes the second surface, it reaches the surface at an angle i and is therefore refracted (or bent) in the direction of the base.
    For thin prisms, which include most prisms in ophthalmic optics, the refraction at the second surface depends primarily on the apical angle (a) of the prism and the refractive index (n) of the material. In practice, the angle of incidence at the first surface will affect the extent to which light is deviated by the prism. The amount of deviation, in degrees, is given by the angle (d), while d = i' - i.

    Moreover, the angles of incidence (i) and refraction (i') are related by the refractive index (n) of the prism material according to Snell's law. For a thin prism, with a relatively small apical angle (a), it can be shown that the approximate deviation (d), in degrees, is given by:
    d = (n - 1) × a
    For small amounts of deviation, 1 degree of deviation is roughly equal to 1.75 prism diopters. For prisms made from hard resin, the refractive index (n) is 1.500. This simplifies our formula even further, since 1.500 - 1 = 1/2. Consequently, for prisms made from hard resin, the deviation in degrees is roughly equal to half the apical angle.
    For example, consider a ray of light from an object point passing through a hard resin prism (n = 1.500) with an apical angle of 10°. The deviation (d) of this ray is equal to (n - 1) × a = (1.500 - 1) × 10 = 5°. This is approximately 8.75 prism diopters.

    I don't understand whether the angle of deviation depends on a the angle of incidence in a thin prism or not?
    Is the thin prism always in the position of minimum deviation?


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  3. #2  
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    It does depend on the angle of incidence, but since the apical angle is small, it is not as dependent as a thicker prism.

    Calculating the Deviation Angle For a Prism
    When the incidence angle and the emergence angle are the same, the prism is said to be in the position of minimum deviation, for a given wavelength


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  4. #3  
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    It does depend on the angle of incidence, but since the apical angle is small, it is not as dependent as a thicker prism.
    Could you tell me how??
    I drew a graph to express the relation between the angle of incidence and that of deviation and that was the result
    graphio.jpg

    That's completely contradictory!!!
    How to prove that the angle of deviation is not dependant on the angle of incidence in a thin prism??
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  5. #4  
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    <br>It does depend on the angle of incidence, but since the apical angle is small, it is not as dependent as a thicker prism.<br>
    <br>Could you tell me how??<br>I drew a graph to express the relation between the angle of incidence and that of deviation and that was the result<br><img src="attachment.php?attachmentid=134&amp;stc=1" attachmentid="134" alt="" id="vbattach_134" class="previewthumb"><br><br>That's completely contradictory!!!<br>How to prove that the angle of deviation is not dependant on the angle of incidence in a thin prism??
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  6. #5  
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    What is contradictory about it? Graph the same thing for a larger apical angle a and I think you will see that the curve is steeper. Small angle a being less steep means the "thinner" the prism the less the deviation depends on incidence angle.
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  7. #6  
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    Yeah I understand
    But Is this because a thin prism looks like a parallelelorgram?
    A parallelogram doesn't deviate light since it is parallel
    ,a thin prism deviates light a little bit because the sides of a thin prism are "about to be parallel" since the apical angle is very small
    is that right?
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  8. #7  
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    it has a lot to do with all the paths the signal takes...for example,the varying thickness presents various harmonic type properties(the angle of the exit plane is different due to wave properties of signal)due to it taking all paths available,and when these signal are summed,the refraction index is observed..
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