Answer:The 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 given by the formula:
m_obj = f_obj / u_obj
where f_obj is the focal length of the objective lens and u_obj is the distance between the object being observed and the objective lens. The magnification of the eyepiece is given by the formula:
m_eyepiece = f_eyepiece / u_eyepiece
where f_eyepiece is the focal length of the eyepiece and u_eyepiece is the distance between the eyepiece and the image formed by the objective lens.
In this problem, we are given the focal lengths of the eyepiece and the objective lens, as well as the distance between them. We can use these values to calculate the magnifications of the individual lenses:
m_obj = 0.415 cm / (18.5 cm - 0.415 cm) = 0.023
m_eyepiece = 2.60 cm / (25 cm + 2.60 cm) = 0.094
where we have used the thin lens formula to calculate the distance between the image formed by the objective lens and the eyepiece (u_eyepiece), which is given by:
1 / u_eyepiece = 1 / (f_obj) + 1 / (f_eyepiece)
Substituting these values into the formula for the overall magnification of the microscope, we get:
m_total = m_obj * m_eyepiece = 0.023 * 0.094 = 0.002
So the overall magnification of the microscope is approximately 0.002, or 2x when expressed as a linear magnification.
Step-by-step explanation: