PAGE References to Optical Formulas Tutorial:  (first reference is to edition 1 / second reference is to edition 2).

Prism definitions.

If you were to cut that prism that you are using for the demonstration down the middle from apex to base you would be able to place it on a protractor and measure the angle that the two sides have to each other. That is the apical angle. This is one of the four prism units; it is not a very useful number by itself because the material that the prism is made from is as important as the angle.

The deviating angle is literally a measurement of how far the ray deviates from its path when it passes through the prism. The deviating angle IS a useful measurement or definition.

The amount a ray will be deviated when it passes through the prism depends on

• the apical angle;
• the index of refraction of the material (and the material surrounding it);
• the wavelength of the ray;
• the angle from which the ray approaches the prism.

Read the discussion on page (73 / 95-96) of the Optical Formulas Tutorial, and do the exercises at the bottom of the page.

Here are a few more for practice:

1. What angle of deviation would a ray have after going through a crown glass prism that has an apical angle of 12 degrees?
2. If a prism is to deviate light by 8 degrees and will be made out of a material with an index of refraction of 1.66, what angle must the prism have at the apex?
3. A prism deviates an incident ray of light by 6 degrees, and the apical angle of the prism is 10 degrees. What is the index of refraction of the material the prism is made of?

The prism diopter and the centrad are the definitions that are currently the most useful. We use the prism diopter because we are generally using relatively weak prisms (under 15 diopters). People who design optical equipment use the centrad because it is more accurate for high power prisms. Both of these definitions are based on how far the image appears to move when the object is viewed through the prism. The prism diopter gives a good approximation of the centrad for prisms up to 15 diopters.  The centrad is the most accurate measurement.  [For strong prisms the prism diopter over-estimates the power of the prism;  the prism diopter estimate is stronger than the more accurate centrad.]

Read through pages (74-76 / 93-98) in the Optical Formulas Tutorial, and do the exercises on those pages.

Does the 'tan' in the formulas on look familiar? If you need to, review the trigonometry part of the first module.

Here are some more exercises:

1. What deviating angle will a 7 diopter prism have?
2. What apical angle will you need for a 2.5 diopter prism made of a plastic with index of 1.50?
3. If a 5.5 diopter prism has an apical angle of 4 degrees, what is the index of the material that the prism was made of?
4. An object is 1 meter away from a 5 diopter prism. How much does the image appear to be displaced?
5. An object is 3 meters away from the same 5 diopter prism. How much does the image appear to be displaced?
6. An abject is 50 cm from this same 5 diopter prism. How much is the image displaced now?
7. What is the displacement if the object is 12 mm away from the 5 diopter prism?
8. Look at the answers that you just got. If a person is wearing a lens with 3 diopters of prism, look how much the images that the person is looking at are displaced. Now look at question four, where you will see how much the wearer's eye will appear to you to be displaced. Do you think that the casual observer will notice this displacement? (That question is ignoring the fact that the lens will appear to be fairly thick on one edge.)
9. If we have a prism that displaces the image 5 mm when the object is 25 cm away, what power prism do we have?
10. If a 10 diopter displaces an image by 15 cm, how far away is the object?

One last aside, for those of you who are comfortable with the math above: look again at the formula for displacement:

or

The point here is not for you to do the problems this way -- much better to convert displacement to cm and distance away to meters. The point is that the unit 'prism diopter' refers to a displacement that is in a 100 to 1 ratio. For every 100 units the object is from the prism the image will be displaced 1 unit.  If we use inches, a one diopter prism will give one inch of image displacement for every 100 inches of distance from the prism to the object. So, if you see a problem where the units are inches (which I doubt) the formula would be

For the mathematicians/scientists out there who like to watch units, a prism diopter can be thought of as a 100/1 ratio without units, or it can be thought of has having the unit cm/m. Your choice.

Read pages 377(bottom right)-383 in Systems for Ophthalmic Dispensing.  Do exercises 3-15 on page 384.
 

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