An elderly sailor is shipwrecked on a desert island, but manages to save his eyeglasses. The lens for one eye has a power of $+1.20$ diopters, and the other lens has a power of $+9.00$ diopters. (a) What is the magnifying power of the telescope he can construct with these lenses? (b) How far apart are the lenses when the telescope is adjusted for minimum eyestrain?
b. 0.944 m
So in this problem, the person has two lenses of different powers. One is positive, 1.2 doctors and the other one is positive. Nine doctors. So from here, we can actually find the focal length of both of the lenses, which is basically the reciprocal of the power of each. And I have already shown the focal length F one enough to hear. So if one is going to be a zero point 833 0.833 meter and after is going to be 0.111 meter. So if the sailor wants to be like telescope, that actually f one has to be the focal length of the objective. Okay. Hey, 33 and F two has to be the focal length of the eyepiece. Now, from here, we can easily find the magnification for party. So far, for part a, the magnification of the angular magnification of the telescope is for collective objective. Over focal length off eyepiece. This is going to be a 0.833 over 0.111 And this will give me a 7.5. All right now for part B the length of the telescope basically would be the focal length of the objective and focal length of the I Piss, which is 0.833 plus 0.111 meters because 0.944 meters.