PART IV: ESTIMATING THE SIZES OF CELLS
When looking at objects through a compound microscope, it is difficult to get a feel for just how big (or small) they really are. We need some kind of “ruler”. The actual size of an object seen under the microscope can be estimated by first measuring the diameter (“width”) of the viewing field (the circle of light seen through the eye piece). You can then estimate the length of the specimen as a fraction of diameter of the field of view. For example, if you estimate the diameter of the field of view to be, say, 6 millimeters (mm) and you see that the specimen is about half as long as the field is wide, then the specimen is about 3 mm long. To estimate the diameter of the field of view, complete exercises 8 and 9 below. When performing these calculations, it helps to keep in mind that the higher the power, the smaller the diameter of the field of view. Always!
6.7 Exercise 7 – Calculating total magnification of objects
1. In the table below, record the magnification of the ocular lens of your compound microscope. It is
engraved on the side of the eyepiece barrel and is usually l0X. When nothing is indicated, the power is 10X.
a. Power of ocular lens ______
2. Similarly, record below the magnification of each of your objective lenses.
a. Power of objective lenses ______ ______ ______ 3. To calculate total magnification, simply multiply the magnification of the ocular lens by the
magnification of the objective lens. Compute the total magnification for each objective lens on your microscope:
Power setting Magnification of objective lens x
Magnification of ocular lens =
Total magnification
Low
Medium
High
20
6.8 Exercise 8 – Determining the diameter of the field of view.
1. First determine the diameter of the field of view (circle of light) for the microscope under low power. Place a clear plastic, metric ruler on the microscope stage across the center of the field of view and focus on the ruler with the lowest power objective.
2. Move the ruler so that one of the millimeter lines falls exactly at the edge of the circle of light. Then count the number of millimeter-long spaces needed to get to the opposite side. The diameter is approximately _____ millimeters. (For our purposes you can round off to the nearest whole number of millimeters).
3. The unit commonly used for measuring microscopic specimens is the micrometer (µm), a unit equal to 1/1000 of a millimeter. There are 1000 micrometers (µm) in one millimeter (mm). To convert diameter in mm to diameter in µm, multiply by 1000.
The diameter of your field of view is _____ mm, which is ________ µm.
4. At higher magnifications, the field of view (lighted circle) covers a much smaller portion of the specimen, and the image of the plastic ruler becomes so large that it can no longer be used to measure the field of view. (Try it!). However, the diameter of the field of view under higher magnifications can be calculated from the diameter of the visual field that you measured under low power. This is because as magnification increases, the diameter of the field of view decreases proportionally. Example: The easiest way to think about this is with an example. Suppose you used the ruler and measured the diameter under low power (40x) to be 6 mm. The diameter under medium power (100 power) would be simply 40/100ths of 6 mm. The diameter under high power (450 x) would be simply 40/450ths of 6 mm.
21
Now calculate the actual diameters for your microscope at medium and high power and enter them in Table 2. You can just use the example above and plug in the values for diameter and power you determined for your own microscope. Or you may find it useful to use the boxed equation below… but then again, maybe not!
Unknown diameter = Diameter measured x The power of the low magnification under higher power under low power The power of the higher magnification
Table 2: Relationship between magnification and the diameter of field of view.
Power Total magnification
Diameter of field of view (millimeters) 1
Diameter of field of view (micrometers) 1
Low
mm
µm
Medium
mm
µm
High
mm
µm
1 For our purposes, you can round off to nearest 0.1 millimeters (mm) or 100 micrometers (µm).
6.9 Exercise 9 – Using the diameter of the field of view to measure cells
1. The actual size of any microscopic object can now be estimated by comparing the length of the specimen to the known diameter of the field of view. To estimate the length of a cell as it appears under low, medium, or high power: a. Determine the diameter of the field of view at this power (from Table 2).
b. Estimate the number of cells that would fit, end-to-end, along the diameter of the field of view. (See diagram below.)
c. Divide the diameter of the field by this number. 2. Estimating cell diameters: In the circles below are two imaginary cells. The cell on the left is shown under medium (100x) power. Its length is about 1/8th the diameter of the field. From Table 2, what is the calculated diameter of the field at 100X? _____ µm.
22
So how long is this cell? _____ µm. 100 x 430 x 3. A different species of cell is shown on the right, as it appears under high (430x) power. As you can see, its length is about one half the diameter of the field. From Table 2, what is the diameter of the field of view at high power? _____ µm. So how long is this cell? _____ µm. 4. According to your calculations, the cell on the right is smaller than the cell on the left. But looking at the diagrams, it is the cell on the right that looks larger. How can this be?