2.3 - Magnification & Units

The magnification equation

• Magnification is a measure of how many times bigger an image is than the real object it shows.
• Image size - The size of the cell or structure as it appears in the photograph, drawing, or microscope image.
• Actual size - Its true size (also called the real size).
• Magnification has no units, because it is one size divided by another - a magnification of x100 simply means the image is one hundred times bigger than the real object.
• The image size and actual size must be in the same units. If they're in different units (e.g. image in millimetres, specimen in micrometres), convert one so both match before dividing.

---

Formula for magnification

The equation can be rearranged to find either of the other two quantities:

1. Image size = magnification × actual size
2. Actual size = image size / magnification

A formula triangle is a convenient way to remember these: with image size at the top and magnification and actual size at the bottom, covering up the quantity you want to find leaves the calculation you need.

Worked example - Using the magnification equation

These examples show the magnification equation used in each of its three directions. In every case the image size and the actual size are put into the same units before dividing or multiplying.

Example 1 - Finding an image size

A specimen is 40 μm wide and is viewed at a magnification of x250. Find the width of the image in mm.

---

Example 2 - Finding a magnification

A magnified image is 6 mm wide and the specimen it shows is 0.03 mm wide. Find the magnification.

---

Example 3 - Finding an actual size

A cell measured in a photograph is 45 mm long and the magnification is x300. Calculate the actual size of the cell in μm.