Complete Question
The distance between the objective and eyepiece lenses in a microscope is 19 cm . The objective lens has a focal length of 5.5 mm .
What eyepiece focal length will give the microscope an overall angular magnification of 300?
Answer:
The eyepiece focal length is [tex]f_e = 0.027 \ m[/tex]
Explanation:
From the question we are told that
The focal length is [tex]f_o = 5.5 \ mm = -0.0055 \ m[/tex]
This negative sign shows the the microscope is diverging light
The angular magnification is [tex]m = 300[/tex]
The distance between the objective and the eyepieces lenses is [tex]Z = 19 \ cm = 0.19 \ m[/tex]
Generally the magnification is mathematically represented as
[tex]m = [\frac{Z - f_e }{f_e}] [\frac{0.25}{f_0} ][/tex]
Where [tex]f_e[/tex] is the eyepiece focal length of the microscope
Now making [tex]f_e[/tex] the subject of the formula
[tex]f_e = \frac{Z}{1 - [\frac{M * f_o }{0.25}] }[/tex]
substituting values
[tex]f_e = \frac{ 0.19 }{1 - [\frac{300 * -0.0055 }{0.25}] }[/tex]
[tex]f_e = 0.027 \ m[/tex]
