1. What deviating angle will a 7 diopter prism have?

  P = 7
= ? P = 100 tan ()
7 = 100 tan ()
tan () = 7 / 100 = 0.07
= 4.00 = 4 degrees
2. What apical angle will you need for a 2.5 diopter prism made of a plastic with index of 1.50?

  P = 2.5
  a = ?
= ?
  n = 1.50
We want the apical angle, but we need to know  in order to find it. We have two ways to do this. Either use P = 100 tan () first and then use  = a (n - 1), or use the formula P = 100 tan [a (n-1)]

1st way:

P = 100 tan ()
2.5 = 100 tan ()
tan () = 2.5 / 100 = 0.025
= 1.432

= a (n - 1)
1.432 = a (1.50 - 1) = a (0.50)
a = 1.432 / 0.50 = 2.86 = 3 degrees

2nd way:

P = 100 tan [a (n-1)]
2.5 = 100 tan [a (1.50 - 1) = 100 tan [a (0.50)]
2.5/100 = 0.025 = tan [a (0.50)]
a (0.50) = 1.432
a = 1.432 / 0.50 = 2.86 = 3 degrees




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?

  P = 5.5
  a = 4
=?
  n = ?
Here is another problem where you have a choice of how to proceed.

1st way:

P = 100 tan ()
5.5 = 100 tan ()
tan () = 5.5 / 100 = 0.055
= 3.148

= a (n - 1)
3.148 = 4 (n - 1)
n - 1 = 3.148 / 4 = 0.787
n = 1.79

2nd way:

P = 100 tan [a (n-1)]
5.5 = 100 tan [4 (n - 1)
5.5/100 = 0.055 = tan [4 (n - 1)]
4 (n - 1) = 3.148
n - 1 = 3.148 / 4 = 0.787
n = 1.79




4. An object is 1 meter away from a 5 diopter prism. How much does the image appear to be displaced?

  prism diopter = 5
  displacement = ? cm
  distance away = 1 meter               displacement in cm
diopter = --------------------------
              distance away in m

              displacement in cm
5 diopters = -----------------------
              1 meter

displacement = (5)(1) = 5 cm




5. An object is 3 meters away from the same 5 diopter prism. How much does the image appear to be displaced?

  prism diopter = 5
  displacement = ?
  distance away = 3 meters               displacement in cm
diopter = -----------------------------
              distance away in m

              displacement in cm
5 diopters = --------------------------
              3 meters

displacement = (5)(3) = 15 cm




6. An abject is 50 cm from this same 5 diopter prism. How much is the image displaced now?

  prism diopter = 5
  displacement = ?
  distance away = 50 cm = 0.5 meter               displacement in cm
diopter = -----------------------------
              distance away in m

              displacement in cm
5 diopters = --------------------------
              0.5 meter

displacement = (5)(0.5) = 2.5 cm




7. What is the displacement if the object is 12 mm away from the 5 diopter prism?

  prism diopter = 5
  displacement = ?
  distance away = 12 mm = 0.012 meter               displacement in cm
diopter = --------------------------
              distance away in m

              displacement in cm
5 diopters = --------------------------
              0.012 meter

displacement = (5)(0.012) = 0.06 cm = 0.6 mm




8. Look at the answers for questions 4 - 7. 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.)

 

 

With the glasses sitting in a relatively normal position, the wearer's eye would appear to the casual onlooker to be displaced one-half of one mm from where it really is. Take a look on your cm ruler that you use every day at how much 0.6 mm is.

5 diopter prism
object distance	image displacement
3 meters	15 cm
1 meter	5 cm
1/2 m = 50 cm	2.5 cm
12 mm	0.6 mm

There are two items to keep in mind here.  If a person needs a few diopters of prism in the glasses in order to see better there will not be enough displacement for the casual observer to notice.  The not-uniformely thick edge will be the major cosmetic effect.  However, it is possible to put several diopters of prism into a lens over a blind eye to purposely change it's vertical placement in a positive manner if the eye is noticebly out of line with the seeing eye.
 

9. If we have a prism that displaces the image 5 mm when the object is 25cm away, what power prism do we have?

  prism diopter = ?
  displacement = 5 mm = 0.5 cm
  distance away = 25 cm = 0.25 meter               displacement in cm
diopter = --------------------------
              distance away in m

              0.5 cm
diopters = --------------------------
              0.25 meter

prism diopters = 2




10. If a 10 diopter displaces an image by 15cm, how far away is the object?

  prism diopter = 10
  displacement = 15 cm
  distance away = ?               displacement in cm
diopter = --------------------------
              distance away in m

              15 cm
10 diopters = --------------------------
              distance away in m

distance away = 15/10 = 1.5 meters

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