Question

The objective lens of a microscope has a focal length of 5.5mm. Part A What eyepiece focal length will give the microscope an overall angular magnification of 300

Answer 1

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  $f_e = 0.027 \ m$

Explanation:

From the question we are told that

    The focal length is  $f_o = 5.5 \ mm = -0.0055 \ m$

This negative sign shows the the microscope is diverging light

     The  angular magnification is $m = 300$

     The  distance between the objective and the eyepieces lenses is  $Z = 19 \ cm = 0.19 \ m$

Generally the magnification is mathematically represented as

        $m = [\frac{Z - f_e }{f_e}] [\frac{0.25}{f_0} ]$

Where $f_e$ is the eyepiece focal length of the microscope

  Now  making $f_e$ the subject  of the formula

         $f_e = \frac{Z}{1 - [\frac{M * f_o }{0.25}] }$

substituting values

        $f_e = \frac{ 0.19 }{1 - [\frac{300 * -0.0055 }{0.25}] }$

         $f_e = 0.027 \ m$