My reading glasses have 1.75 diopters. My friend with much better eyes has weaker glasses with only 0.2 diopters. What combined power would I get if I were able to read using both pairs of glasses at the same time, arranging one immediately in front of the other? If I held the lens combination up in the sunlight, how far away would the image of the Sun form (i.e. what is the focal length of the combined lenses)?

I don't know how to approach this and my textbooks seems to lack proper instructions on doing this. If anybody could explain how to do this.. it would be reallly helpful. Thanks!

A diopter is an "inverse meter" measurement of the curvature of light passing through a lens which is suitable for describing simple lenses placed close together (thin lens approximation) as directly affecting the focal distance of a parallel bundle of beams.

For light coming into a lens in a parallel bundle of rays, a flat sheet of glass (0 diopters) will focus the light at a distance of 1/0 meters -- aka it doesn't.

A 0.2 diopter lens will focus the light 1/0.2 meters = 5 meters away.

A 1.75 diopter = 7/4 diopter lens will focus the light 4/7 meters ≈ 0.571 meters away.

The thin lens approximation says you can approximate the effect of two thin lens of a and b diopters placed close together and lined up perfectly as another thin lens of a + b = c diopters.

So the combined power is 0.2 + 1.75 = 1.95 diopters = 39/20 diopters. And the focal length is therefore 20/39 meters ≈ 0.513 meters.

And you can check if Wikipedia explains it better than your textbook.

http://en.wikipedia.org/wiki/Dioptre
http://en.wikipedia.org/wiki/Lens_(optics)...n_lens_equation

sometimes textbook just can't tell u much lol
learn to use Internet, like google, aol. But forum is good choice too.
well, if u decided to change a pair of brand new reading glasses, you can check [Moderator: Commercial URL deleted]