Question

Your little sister currently thinks all things insectoid are really cool, and you want to give her a microscope so she can look at butterfly wings. However, you are a broke college student, so you need to build it yourself. You buy two thin lenses: one with a focal length f = 2.0 cm and the other with f = 1.0 cm.

a. Which lens has a higher power P? You will use this lens as the objective.

b. You’ve built a tube that places the eyepiece 16 cm from the objective. For viewing with a relaxed eye (the image is at your Far Point of infinity), how far should the butterfly wing be from the objective lens?

Answer 1

a) Power is the inverse of the focal length.

P = 1/f

Hence P1 = 1/.02m = 50 D

P2 = 1/0.01 = 100 D

Hence the one with focal length of 1 cm has the higher power.

b. Let the butterfly wing be at a distance x.

Then for the objective lens,

1/f = 1/di + 1/do

1/1 = 1/di + 1/x

=> 1/di = 1 - 1/x = (x-1)/x

or, di = x/(x-1)

The new object distance for the eyepiece will be 16 - di = 16 - x/(x-1) = 15x-16/(x-1)

Therefore,

1/fe = 1/do + 1/di

1/2 = (x-1)/15x - 16 + 0

2x - 2= 15x - 16

18 = 13x

=> x = 18/13 = 1.38 cm