The objective lens and the eyepiece of a microscope have focal lengths of 4.0 mm and 25 mm,respectively.The objective produces a real image 30 times the size of the object,with the final image viewed at infinity.The near point of the microscope user is at 25 cm.What is the magnitude of the overall magnification of the microscope?
A)250
B)300
C)350
D)400
E)450

Question

Quizplus · Accepted Answer

The overall magnification, M, of a microscope is given by the product of the magnification of the objective lens (m_obj) and the magnification of the eyepiece (m_eyepiece):

M = m_obj x m_eyepiece

The magnification of the objective lens is given by:

m_obj = -(di / do)

where di is the image distance and do is the object distance. In this case, the objective produces a real image that is 30 times the size of the object, so:

m_obj = -(di / do) = -30

Since the final image is viewed at infinity, we can assume that the eyepiece acts as a simple magnifying glass, with a magnification given by:

m_eyepiece = (25 cm) / (f_eyepiece)

where f_eyepiece is the focal length of the eyepiece. Substituting the given values, we get:

m_eyepiece = (25 cm) / (25 mm) = 1000

Therefore, the overall magnification of the microscope is:

M = m_obj x m_eyepiece = (-30) x (1000) = -30000

The negative sign indicates that the image is inverted. The magnitude of the overall magnification is 300. Therefore, the correct choice is B.

The Objective Lens and the Eyepiece of a Microscope Have