Microscopy: magnification = size of image size of real object

The idea

This relationship links the apparent size of a specimen seen through a microscope to its true size. Magnification is a ratio, so it has no units; image size and real (actual) size must be measured in the same unit before dividing. Rearranged, image size = magnification × real size and real size = image size ÷ magnification. For example, a cell image 40 mm wide viewed at ×400 has real width 40 mm ÷ 400 = 0.1 mm, which is 100 µm. When using a scale bar, measure the bar and the image in the same units, then divide the bar's measured length by its stated length to find magnification. Always convert units consistently, and give magnification as a plain number, often with a multiplication sign, such as ×400.

What earns the marks

• State the relationship as magnification = image size ÷ real size, recognising that magnification is a ratio and therefore has no unit.
• Rearrange the relationship correctly to find image size (magnification × real size) or real size (image size ÷ magnification) when the other two values are known.
• Convert image and real measurements to the same unit before calculating, for example millimetres to micrometres using 1 mm = 1000 µm.
• Use a scale bar by measuring its printed length and dividing that measured length by the stated length to obtain magnification.
• Interpret a stated magnification such as ×400 as meaning the image is 400 times larger than the real object.
• Present the final answer with a sensible unit for a length or as a plain number for magnification, and show the substitution clearly.

Common mistakes and how to put them right

• Dividing real size by image size instead of image size by real size.

  Put it right by checking that a magnification greater than 1 means the image is larger than the object.

• Mixing units, such as dividing an image in millimetres by a real size in micrometres.

  Put it right by converting both measurements to the same unit first.

• Giving magnification a unit such as mm.

  Put it right by remembering magnification is a ratio comparing two lengths, so units cancel.

Exam tips

• Write the equation triangle or rearrange the relationship before substituting numbers, so the correct operation is clear.
• Convert all lengths to the same unit, often micrometres for cells, and state the conversion you used.
• Check whether the question asks for magnification, image size or real size, and give the answer with the appropriate unit or as a plain number.