Question

A converging lens with a focal length of 4.0cm is to the left of a second identical lens. When a feather is placed 11cm to the left of the first lens, the final image is the same size and orientation as the feather itself.

What is the separation between the lenses?

Express your answer using two significant figures.

Answer 1

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    4   cm
do = object distance =    1.10E+01   cm
di = image distance      
      
Thus, solving for di,      
      
di =    6.285714286   cm

Thus, the magnification, m = -di/do,      
      
m1 =    -0.571428571  

Thus, if x = the distance of separation between the lenses, for the second lens, do = x - 6.2857. Thus,

1/f = 1/do + 1/di      

1/f = 1/(x - 6.2857) + 1/di      

As m1 m2 = 1, Then m2 = -1.75. Thus,

-di/do = -1.75

di = 1.75do

Thus,

1/f = 1/(x - 6.2857) + 1/di      

becomes

1/f = 1/(x - 6.2857) + 1/[1.75(x - 6.2857)]

1/4.0 = 1/(x - 6.2857) + 1/[1.75(x - 6.2857)]
      
Solving for x,

x = 12.57 cm   [ANSWER, DISTANCE OF THE TWO LENSES]