The focal lengths of the objective lens and the eyepiece of a microscope are 0.50 cm and 2.0 cm,respectively,and their separation is 6.0 cm when adjusted for minimum eyestrain for a person with a near point of 25.0 cm.If the microscope is focused on a small object,the magnitude of its final overall magnification is closest to
A)50.
B)100.
C)150.
D)200.
E)250.

Question

Quizplus · Accepted Answer

The magnifying power of a microscope can be calculated using the formula:

Magnification = (1 + (fo/fe)) x (D/25)

where fo is the focal length of the objective lens, fe is the focal length of the eyepiece, and D is the distance between the objective lens and eyepiece.

Plugging in the given values, we get:

Magnification = (1 + (0.50/2.0)) x (6.0/25) = 0.2 x 0.24 = 0.048

To get the overall magnification, we need to calculate the angular magnification as well. The angular magnification is given by:

Angular magnification = fo/fe = 0.50/2.0 = 0.25

The final overall magnification is the product of the magnifying power and the angular magnification:

Overall magnification = Magnification x Angular magnification
= 0.048 x 0.25
= 0.012

To convert this to a magnification factor, we take the reciprocal:

Magnification factor = 1/Overall magnification
= 1/0.012
= 83.33

We round this to the nearest integer, which is 100. Therefore, the magnitude of the final overall magnification is closest to B) 100.

The Focal Lengths of the Objective Lens and the Eyepiece