Chapter 25, Problem 49P

To determine

The resolving power of the given microscope.

Answer to Problem 49P

Solution:

The resolving power of the microscope is found to be 1200 nm .

Explanation of Solution

If two objects are closely spaced are distinguishable, then they are said to be resolved. The resolving power of a microscope is the minimum separation of two objects that can be resolved. The resolving power of a microscope depends on the diameter of the objective, its focal length and wavelength of the light used.

Given:

The wavelength of light used, $\lambda =550\text{ nm}$

The diameter of the objective, $D=5\text{ mm}$

The focal length of the objective lens, $f=9\text{ mm}$

Formula:

The resolving power of the microscope is given by

  $RP=\left(\frac{1.22\lambda f}{D}\right)$

Calculation:

Substitute the given values of the focal length, diameter and the wave length of light in the expression and calculate the resolving power.

  $\begin{array}{c}RP=\left(\frac{1.22\lambda f}{D}\right)\end{array}$

    $\begin{array}{c}=\frac{\left(1.22\right)\left(550\text{ nm}\right)\left(9\text{ mm}\right)}{\left(5\text{ mm}\right)}\end{array}$

    $\begin{array}{c}=1207.8\text{ nm}\end{array}$

Conclusion:

Using the expression for the resolving power, the resolving power of the given microscope is found to be 1200 nm.