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EK Method for Optics


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Hey all!


I'm a bit confused with the EK method for optics. I know there's also a BR one, as described in the following:


That worked really well on a paper exam. The problem with drawing on a CBT exam is that it wastes time and isn't necessary. On a paper exam, you can write right next to the question, keeping the question in view the whole time. But when using scratch paper, drawing requires going back and forth between question and the picture. Even if it's only five to ten seconds wasted looking back and forth, it adds up over the duration of the exam. For many test-takers it's not a big deal, but why not learn to do things more efficiently and in your head if you can? We (TBR) emphasize in our classes visualizing things in your head and using shortcuts. Lens and mirrors have some of the very best short cuts of any topic.


We have two ways to answer these questions in fifteen seconds or so that require no drawing at all. I'm going to walk a fine line here, because these are proprietory methods we teach in our lectures. If you do enough lens and mirror examples you'll see a pattern.


For a diverging system, think of the word "Divirtual." No matter whether it's a lens or a mirror, a diverging system generates a virtual image that is within the focal point (making it smaller).


For a converging system, lens or mirror, you need to visualize the object position in terms of distinct regions.


Region I Object beyond R leads to an image between f and R (IR/Smaller)

Region II Object at R leads to an image at R (IR/Same size)

Region III Object between f and R leads to an image beyond R (IR/Larger)

Region IV Object at f leads to an image at infinity (no image)

Region V Object between f and f/2 leads to an image beyond f (UV/Larger)

Region VI Object between f/2 and lens leads to an image between f and the lens (UV/Larger)


Draw all six of these on the same picture and then visualize this summary.

Once you do this, you'll not need to draw ray diagrams, and instead can simply visualize where the object and corresponding image correlate. It becomes easy from this point to zero in on the best answer. Consider the following questions:


1) Object at 12 cm with R =18 cm; convex len. The image is:

a) UV at 36 cm

B) IR at 12 cm

c) IR at 18 cm

d) IR at 36 cm


Sol'n: Convex lens = converging system, therefore use summary picture.

If R is 18, then f if 9, so object (at 12) is in Region III. Image forms beyond R, so it's IR and greater than 18. Only choice D fits.



2) 10 cm tall object at 20 cm with f =8 cm; concave mirror. Where is image and how tall is it?

a) 3 cm tall at 6 cm

B) 12 cm tall at 9.3 cm

c) 6.7 cm tall at 13.3 cm

d) 20 cm tall at 40 cm


Sol'n: Concave mirror = converging system, therefore use summary picture.

If f is 8, then R if 16, so object is in Region I. Image forms between f and R, so it's smaller in size (because it's closer to the mirror than the object) and found between 8 and 16. Only choice C fits both criteria.


3) Object at 50 cm with R =40 cm; convex mirror. The image is:

a) UV at -14.3 cm

B) UV at -33.3 cm

c) IR at +14.3 cm

d) IR at +33.3 cm


Sol'n: Convex mirror = diverging system, therefore think "DIVIRTUAL."

Image is UV, so C and D are out. Image must form within f, so image distance must have an absolute value less than 20. Only choice A fits.


This method works well with multiple choice questions only, but luckily the MCAT is multiple choice. It is an easy method that can be picked up with just a little practice.


The second method involves math and is very simple and can be done in your head in five to ten seconds. If you are really troubled by this topic, I don't mind sharing it via PM. I just don't want to expose too many of our tricks to our competitors.


But this also confuses me (especially the different regions for a converging system... what is "R"?).


What's the best method you bright folks have used for optics? Is it worth investing time into learning either the EK, BR, or TPR methods - or is there an even better one?



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