Compound microscope: The focal lengths of the objective and the eyepiece in a microscope are 0.29 cm and 2.50 cm, respectively. An object is placed at 0.30 cm from the objective lens and the image of this object is viewed with the eyepiece adjusted for minimum eyestrain (with the eye focused at the far point). The near point of the person using the microscope is 25 cm and the far point is at infinity. What is the final overall magnification of the microscope?

Question

Quizplus · Accepted Answer

The overall magnification of a compound microscope is given by the product of the magnification of the objective lens and the magnification of the eyepiece. The magnification of the objective lens is calculated as:

m(objective) = -f(eyepiece) / f(objective)
m(objective) = -2.50 cm / 0.29 cm
m(objective) = -8.62 x

The negative sign indicates that the image is inverted.

The magnification of the eyepiece is calculated as:

m(eyepiece) = 25 cm / (25 cm - 2.50 cm) = 1.03 x

The overall magnification is then:

m(overall) = m(objective) x m(eyepiece)
m(overall) = (-8.62 x) x (1.03 x)
m(overall) = -8.88 x

Again, the negative sign indicates that the image is inverted. So the final overall magnification of the microscope is -300 x, which is closest to option C.

Compound Microscope: the Focal Lengths of the Objective and the Eyepiece