A 2.0-cm-tall object is 21cm in front of a convex mirror that has a -59cm focal

Question

A 2.0-cm-tall object is 21cm in front of a convex mirror that has a -59cm focal length.

Part A

Calculate the position and height of the image.

s' = ___________ cm , h' = ________________cm

Part B

State whether the image is in fornt of or behind the mirror, and whether the image is upright or inverted.

a) The image is upright adn placed in front of the mirror.

b) The image is inverted and placed in front of the mirror.

c) The image is inverted and placed behind the mirror.

d) The image is upright and placed behind the mirror.

Explanation / Answer

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    -59   cm
do = object distance =    21   cm
di = image distance      
      
Thus, solving for di,      
      
di =    -15.4875   cm   [ANSWER, PART A, image distance]
      
Thus, the magnification, m = -di/do,      
      
m =    0.7375  
      
Thus, as  
  
hi =    2   cm
      
And hf = m * hi, then      
      
hf =    1.475   cm    [ANSWER, PART A, image height]

***************************

As di < 0, it is behind the mirror.

As m > 0, it is upright.

Thus, the answer is OPTION D.   [ANSWER]

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