Question

If you treat a 14 × eyepiece of a microscope as a magnifying glass that produces an image at infinity, what is its focal length? The microscope is designed for an image distance of 172 mm from the objective, and the objective is marked 25 ×. What is its focal length?

Answer 1

Given:

magnifying power of the eyepiece M_e = 14

magnifying power of objective M_o = 25

image distance from the objective v_o = 172 mm

Let the focal length of the eyepiece be f_e and the focal length of the objective be f_o

For a mgnifying glass, magnifying power, M is given by

where D is the least distance of distinct vision, D = 25 cm for human eye, and f is the focal length of the magnifying glass.

For the given eyepiece:

f_e = 1.9 cm

for a compound microscope, magnification factor M is given by

where u_o is object distance from objective

also M = M_e * M_o = 14 * 25 = 350

u_o = 6.88 mm

f_o = 6.62 mm