You are in biology class and wish to look at a slide of petrified wood. The micr

Question

You are in biology class and wish to look at a slide of petrified wood. The microscope you are assigned has only two lenses: an objective lens and an eye piece. The objective lens has a focal length of 4.5 mm and the eyepiece has a focal length of 10.0 mm (both are convex lenses). The distance between the two lenses is 20 mm. If the object viewed by the objective lens is 1.0 mm in height and is 7.0 mm away from the objective lens:

a.) Find the final image distance of the object.

b.) Find the height of hte final image.

Explanation / Answer

for objective lens ::

f = 4.5 mm

do = object distance = 7 mm

using lens equation ::

1/di + 1/do = 1/f

1/di + 1/7 = 1/4.5

di = 12.6 mm

magnification is given as ::

m = -di/do = -12.6 /7 = -1.8

negative sign suggest that image is inverted

image height = m x object height = 1.8 x 1 mm = 1.8 mm

distance between the two lens = 20 mm

so distance of image from the eyepiece = 20 mm - 12.6 mm = 7.4 mm      to left of eyepiece

for eyepiece ::

do = object distance = 7.4 mm

f = focal length = 10 mm

using lens equation ::

1/di + 1/do = 1/f

1/di + 1/7.4 = 1/10

di = - 28.46 mm        to left of eyepiece

distance of object from eyepiece = 7 + 20 = 27 mm

final image distance from object = 28.46 - 27 = 1.46 mm

magnification is given as ::

m = -di/do = -(-28.46)/7.4 = 3.85

positive sign suggest that image is upright

image height = m x object height = 3.85 x 1.8 mm = 6.93 mm

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