Prism question

[Pam]

I am helping several of my co-workers study for the ABO, and we came across this question that I cannot figure out. Here it is:

A lens is surfaced with 3 prism diopters base up and in at 45 degrees combined with 4 prism diopters base up and out at 95 degrees. What is the amount and direction of the resulting prism?
a. 6.5 base up and in at 74 degrees
b. 5.5 base up and in at 54 degrees
c. 4.5 base up and out at 74 degrees
d. 6.5 base up and out at 74 degrees

This one has really stumped us all, and I know it is probably not a vital question to passing the exam (I did and I have no clue about this one!) but now I just have to know! Thanks!

[David Wilson]

Pam,
The answer is a) There is a neat formula that will allow you to do this (I'll put it below) but there is a way you can do this quickly by elimination, which is the way most multiple choice questions are best attempted when calcs are involved. The fact that the question says 45 up and in and 95 up and out tells us that this is a right eye (up and out, for example, for a LE would be between 0 and 90). We can now eliminate answers c and d since a right eye cannot have up and out at 74. Now for the last two choices, the resultant must lie between the two angles 45 and 95. It will lie closer to the 95 than the 45 since there is 4 prism dioptres at 95 and only 3 at 45. Only one answer fits the bill and that is a. Now for the formulae.
V prism = 3sin45 + 4sin95
H prism = 3cos45 + 4cos95
Once you have the vertical and horizontal prismatic effects it is a simple matter of compounding the prisms to achieve the 6.5 (6.4 actually)at 74 degrees up and in.
I hope that this helps, Pam.
Regards
David

[Darryl Meister]

Nicely stated, David.

Best regards,
Darryl

[Blake]

6.35822 at 73.8111 degrees - but who cares!
:-)

If you've got a sheet of graph paper and a protractor, you can get a visualization of what's going on. Draw a 3 inch (or cm or whatever) line at 45 degrees, and a 4 inch (cm, etc.) line at 95 degrees. Then, at the end of the 3 in. line draw another 4 inch line parallel to the first, and draw a 3 inch line parallel to the first, so that you have a parallelogram (looks like a rectangle leaning over). Now draw a line along the longer diagonal. Lo and behold! The diagonal line will be about 6.4 inches, at about 74 degrees...

Blake

[stephanie]

I don't know the answer to your question Pam, but I just wanted to post to tell you how great I think it is that you are passing on your abo knowledge!!! I am helping someone via internet. Great job!!! KEEP PASSING IT ON!!! It makes you do a better job as well as your co-workers!!

Have a great day!!!
Steph

[Pam]

Thank you to everyone who helped me out with this one. I think I am not going to confuse my "students" with this one - they have enough to learn in the next month and a half! Steph, I feel like I know so much more and I have a better understanding of it now that I have to teach it to other people. I wish I knew all this last May! I could probably really rock that ABO test now! Maybe in a few years I'll try that advanced one...

[Darryl Meister]

Hi Pam,

In all fairness, your co-worker really shouldn't expect to see this caliber of question until the Master-level (Advanced) exam. And, even then, you may not after they've watered it down over the years. For the basic ABO exam (NOCE), I would suggest that she becomes adept at Prentice's rule, splitting prisms between both eyes, and how slab-off prism is used.

Best regards,
Darryl

[Pam]

Thanks Darryl, I was pretty sure they wouldn't need to know it for the test, but it was in our study materials and you just never know when it may come in handy! :) I have printed out the answers given in this post and I will put them in my book o' optical information incase I ever need it. Thanks again!

[Vicki]

Hi Pam,
I did have some resultant prism questions on my state board test here in S.C. several years ago.

[stephanie]

Pam, I agree with you on that one. I can certainly see a lot of the errors I made now and why. I guess that is why you should never stop learning. It is the key not only to optical to life. I enjoy learning all I can.
Have a great day and keep up the good work!
Steph