Marooned on a desert island and with a lot of time on your hands, you decide to

Question

Marooned on a desert island and with a lot of time on your hands, you decide to disassemble your glasses to make a crude telescope with which you can scan the horizon for rescuers. Luckily you're farsighted, and, like most people, your two eyes have different lens prescriptions. Your left eye uses a lens of power +4.5D (diopters = 1/f), and your right eye's lens is +3.0D. a. Which lens should you use for the objective and which for the eyepiece? b. What will be the overall magnification of this telescope? c. How far apart should the two lenses be when you focus on distant objects?

Explanation / Answer

Given

the focal length of the lenses is

   left eye fl =    1/4.5 = 0.222 cm

   right eye fr = 1/3 = 0.333 cm

in order to see the horizon the telescope should have the eye piece of short focal length
a)

so the objective lens is of larger focal length that is right eye lens is objective lens and left eye lens as eye piece

b) the over all magnification is m = f0/fe

   m = 0.333/0.222 = 1.5

c)
the distance between the lenses is d = f0+fe = 0.333+0.222 = 0.555 cm

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