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Thread: Prism Calculation

  1. #1
    Master OptiBoarder keithbenjamin's Avatar
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    Prism Calculation

    I need someone to tell me if I've done this right...

    Trying to calculate prism in diopters given an index of refraction and the angle of a flat prism.

    Prism angle = 4.1 deg
    I = 1.52

    If light is incident perpendicular to the front surface of the prism, the incident angle on the back side will be equal to the prism angle or 4.1 deg.

    First determine the exit angle (theta) using Snell's law:

    1.52 = sin(4.1)/sin(theta)

    sin(theta) = sin(4.1)/1.52

    theta = arcsin(0.047)

    theta = 2.7 deg

    Second using the trig formula for tan to determine the deviation at 100cm:

    tan(2.7) = x/100cm

    x = tan(2.7)(100cm)

    x = 4.7cm or 4.7 prism diopters


    thanks

    Keith

  2. #2
    Master OptiBoarder Darryl Meister's Avatar
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    At first glance, I would say that you have your variables reversed in Snell's law.

    Since the angle of incidence is 4.1 deg within the lens material (I = 1.52), your formula should look like:

    1.52 * sin 4.1 = 1 * sin theta

    Since the medium containing the angle of incidence (4.1 deg) has a refractive index of 1.52 and the medium containing the angle of refraction (theta) has a refractive index of 1 (air). Therefore, theta is given by:

    theta = arcsin(1.52 * sin 4.1)

    Once you calculate theta, which should be about 6.239 deg, you need to subtract the angle of incidence to get the final angle of deviation:

    Deviation = 6.239 - 4.1 = 2.139 deg

    This agrees with the thin prism approximation, which is:

    Deviation = (I - 1) * Prism Angle

    Deviation = (1.52 - 1) * 4.1 = 2.132 deg

    From this angle of deviation, you can calculate your prism diopters, as you have done.

    Best regards,
    Darryl

  3. #3
    Master OptiBoarder keithbenjamin's Avatar
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    Thanks Darryl, you're the best.

    Love the thin prism approximation... just a tad simpler. ;)

  4. #4
    Master OptiBoarder Darryl Meister's Avatar
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    Glad to help. Keep in mind that if you're in a hurry for answers like that, you might get them a little faster if you also post the question in the Ophthalmic Optics forum. ;)

    Best regards,
    Darryl

  5. #5
    Master OptiBoarder keithbenjamin's Avatar
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    Thanks for reminding me.

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