thin lens questions please show work. thank you! You have a converging thin lens

Question

thin lens questions please show work. thank you!

You have a converging thin lens (focal length = 30.0 cm) and a convex spherical mirror (radius = 1.00 m). You also have a table lamp. The lens is placed between the lamp and the minor, is 35.0 cm from the lamp, and 2.00 m from the minor. Find the position of the image produced by the lens, Find the position of die image produced by the minor, measured from the minor. Is this image real or virtual? Find the overall magnification of this optical system. Is the final image upright or inverted?

Explanation / Answer

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    30   cm
do = object distance =    3.50E+01   cm
di = image distance     
      
Thus, solving for di,      
      
di =    210   cm   [ANSWER, PART A]
      
Thus, the magnification, m = -di/do,      
      
m =    -6  

Thus, for the mirror,

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    -50   cm
do = object distance =    -1.00E+01   cm
di = image distance     
      
Thus, solving for di,      
      
di =    12.5   cm    [ANSWER, PART B, REAL, as di > 0]
      
Thus, the magnification, m = -di/do,      
      
m =    1.25

Thus, the overall magnification is

mtot = m1 m2 = -6 (1.25)

mtot = -7.5   [ANSWER, INVERTED as mtot < 0, PART C]

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