Calculating Actual Size
- When using microscopes to study biological specimens, it is possible to calculate the actual size of organisms, cells, and parts of cells
- The actual size of specimens can be calculated using the magnification and the measured size of an image as follows:
Actual size = image size ÷ magnification
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- Magnification is sometimes provided in an exam question stem
- Magnification can be calculated from the scale bar of an image
- Sometimes magnification is calculated from information about the magnification of the eyepiece lens and the objective lens
- Remember that the equation above is part of the equation triangle from calculating magnification
Worked example
Using a scale bar to calculate actual size
A lab technician observed bacterial cells with an electron microscope, and produced the image below.
The scale bar measures 2 cm in length, and the length of the technician's image of one bacterial cell measures 7.6 cm.
Use the information provided to calculate the actual length of a bacterial cell in the image.
Step 1: Use the scale bar to calculate the magnification of the image
The equation triangle for magnification tells us that:
Magnification = image size ÷ actual size
The scale bar measures 2 cm = 20 mm = 20 000 μm
The scale bar represents an actual size of 1 μm
Magnification = 20 000 ÷ 1
= 20 000
Step 2: Substitute values into the equation for actual size
Actual size = image size ÷ magnification
The question stem tells us that one cell = 7.6 cm = 76 mm = 76 000 μm
Magnification is ×20 000
Actual size = 76 000 ÷ 20 000
= 3.8
Therefore, the actual length of a bacterial cell in this image is 3.8 μm
Worked example
Using lens magnification to calculate actual size
A scientist looked at a sample of red blood cells under a light microscope.
The eyepiece lens of the microscope had a magnification of ×10 and the objective lens had a magnification of ×40.
The scientist produced a photomicrograph of the blood cells, shown below, in which the red blood cells have an average diameter of 3 mm when measured using a ruler.
Calculate the average diameter of the red blood cells in the sample. Give your answer in micrometres.
Step 1: Calculate the total magnification of the specimen
total magnification = eyepiece lens magnification × objective lens magnification
10 × 40 = 400
Magnification = ×400
Step 2: Convert the image size into μm
1 mm = 1000 μm
3 × 1000 = 3000
Image size = 3000 μm
Step 3: Substitute values into equation for actual size
Actual size = image size ÷ magnification
Actual size = 3000 ÷ 400
= 7.5
Therefore, the average size of a red blood cell in this sample is 7.5 μm
Examiner Tip
Note that you would be expected to use your own ruler to provide image size measurements in actual size calculations.
Don't forget to convert units in calculations like this!
