Question

Two converging lenses, each of focal length 14.9 cm, are placed 39.8 cm apart, and an object is placed 29.1 cm in front of the first. How far from the first lens is the final image formed? Answer in units of cm.

What is the magnification of the system?

Answer 1

For the first lens:

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    14.9   cm
do = object distance =    29.1   cm
di = image distance      
      
Thus, solving for di,      
      
di =    30.53450704   cm
      
Thus, the magnification, m = -di/do,      
      
m =    -1.049295775  

For the second lens, the object distance is 39.8 - 30.5345 cm:

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    14.9   cm
do = object distance =    9.2655   cm
di = image distance      
      
Thus, solving for di,      
      
di =    -24.50189901   cm
      
Thus, the magnification, m = -di/do,      
      
m =    2.644422753  

Thus, this image is

39.8 - 24.502 cm = 15.3 cm from the first lens. [ANSWER]

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The total magnification is the product of the individual magnification,

mtot = -1.04929*2.644422 = -2.77 [ANSWER]