A 4.0-cm-tall object is 80cm in front of a converging lens that has a 40cm focal

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4.0-cm-tall object is 80cm in front of a converging lens that has a 40cm focal length.

Problem 18.30 A 4.0-cm-tall object is 80 cm in front of a converging lens that has a 40 cm focal length. Part A Calculate the image position. Express your answer to two significant figures and include the appropriate units. Part B My Answers Give Up Calculate the image height. Type a positive value if the image is upright and a negative value if it is inverted. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

  this is a very straightforward problem in optics

use the basic lens equation:

1/p + 1/q = 1/f

p=object distance = +80 cm
q=image distance
f=focal length = + 40 cm

1/80 + 1/q = 1/40

1/q = 1/40-1/80 = 1/80

q=80 cm, so the image is 80 cm behind the converging lens (the sign convention for converging lenses is that positive image distances are behind the lens; positive object distances are in front of the lens)

the magnification is given by m = -q/p =-80/80 = -1

this means the image has the same height as the object and is inverted

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