A compound microscope is made with an objective lens ( = 0.90 cm) and an eyepiece ( = 1.1 cm). The lenses are separated by a distance of 10 cm. If an object is 1.0 cm in front of the objective lens, where will the final image of the eyepiece be located?
A)−30
B)−15
C)−23
D)−11
E)−9

Question

A compound microscope is made with an objective lens (  = 0.90 cm) and an eyepiece (  = 1.1 cm). The lenses are separated by a distance of 10 cm. If an object is 1.0 cm in front of the objective lens, where will the final image of the eyepiece be located?
A)−30 
B)−15 
C)−23 
D)−11 
E)−9

Quizplus · Accepted Answer

Using the formula for compound microscopes:

m = −d/f_obj = d/f_ep

where m is the magnification, d is the distance between the lenses, f_obj is the focal length of the objective lens, and f_ep is the focal length of the eyepiece.

Rearranging, we get:

f_ep = (d/m) - f_obj

We are given f_obj = 0.90 cm, f_ep = 1.1 cm, and d = 10 cm.

To find the magnification, we use the formula:

m = (image distance)/(object distance) = (distance from eyepiece to image)/(distance from objective to object)

We know that the object distance is 1.0 cm in front of the objective lens, so:

m = (distance from eyepiece to image)/(10.0 cm)

To find the distance from the eyepiece to the image, we use the formula:

1/f = 1/do + 1/di

where f is the focal length of the eyepiece, do is the distance from the eyepiece to the intermediate image, and di is the distance from the intermediate image to the final image.

For a compound microscope, the intermediate image is located at a distance of f_obj in front of the eyepiece. So:

do = 10.0 cm - 0.90 cm = 9.10 cm

Substituting in the values and solving for di, we get:

1/1.1 = 1/9.10 + 1/di

di = -10.9 cm

(Note the negative sign, which indicates that the image is virtual.)

Substituting into the formula for magnification, we get:

m = (-10.9 cm)/(1.0 cm) = -10.9

Substituting into the formula for the focal length of the eyepiece, we get:

f_ep = (10.0 cm/-10.9) - 0.90 cm ≈ -11 cm

Therefore, the final image of the eyepiece will be located at a distance of -11 cm, or 11 cm to the left of the eyepiece (as indicated by the negative sign).

So the answer is D, -11.

A Compound Microscope Is Made with an Objective Lens