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

To find the position of the final image, we need to use the formula for the magnification of a compound microscope:

M = (L / f1) × (1 + d / f2)

where 
L = distance between the lenses (10 cm)
f1 = focal length of objective lens (0.90 cm)
d = distance of object from objective lens (1.0 cm)
f2 = focal length of eyepiece (1.1 cm)

Plugging in the values and solving for the position of the final image, we get:

M = (10 / 0.90) × (1 + 1 / 1.1)
M = 13.95

Since the magnification is positive, the final image is upright. The position of the final image is given by:

di = (M × f1) + (d - f1)
di = (13.95 × 0.90) + (1.0 - 0.90)
di = 11.55 cm

Therefore, the final image of the eyepiece will be located 11.55 cm behind the eyepiece, which is equivalent to a distance of -11 cm relative to the objective lens. Hence, the answer is D (-11).

A Compound Microscope Is Made with an Objective Lens