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A 4.0 cm tall object is 5.0 cm in front of a diverging lens with a focal length

ID: 1380646 • Letter: A

Question

A 4.0 cm tall object is 5.0 cm in front of a diverging lens with a focal length of -6.0cm. A converging lens with a focal length of 6.0 cm is located 8.0 cm behind the diverging lens. Use ray tracing to draw image 1 and image 2 (the final image), and determine di 2 and hi2. Use the thing lens equation to verify your results and calculate the total magnification mt. Is image 1 real or virtual, upright or inverted, reduced or enlarged. Classify image 2 as well, relative to both image 1 and to the original object.

Explanation / Answer

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    -6   cm
do = object distance =    5   cm
di = image distance      
      
Thus, solving for di,      
      
di =    -2.727272727   cm
      
Thus, the magnification, m = -di/do,      
      
m =    0.545454545  

Which is 10.7272 cm to the left of the converging lens.

Thus, it is VIRTUAL, ERECT, REDUCED. [ANSWER]

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Thus, for he second lens,

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    6   cm
do = object distance =    10.7272   cm
di = image distance      
      
Thus, solving for di,      
      
di =    13.61550178   cm
      
Thus, the magnification, m = -di/do,      
      
m =    -1.269250296  

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Thus, for the final image,

mtot = m1 m2 = 0.5454 * -1.269

mtot = -0.6923 [ANSWER]

Also,

di2 = 13.62 cm
hi2 = h mtot = -2.769 cm

which is REAL, INVERTED, REDUCED.    [FINAL IMAGE]

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