Magnification and Scale Calculations
Use magnification as image size divided by actual size, and convert between millimetres, micrometres and nanometres without losing a factor of a thousand. Includes reading a scale bar and choosing a light or electron microscope by the detail needed.
What a learner can do afterwards
- Rearranges the magnification relation to find any one of the three quantities.
- Converts a length between millimetres, micrometres and nanometres and keeps the units on the answer.
- Uses a scale bar on a micrograph to state the real width of a cell.
1 · Read
A flea photo can show it as big as your hand, but the flea has not grown. Magnification tells you how many times bigger the image is than the real thing. You find it with one rule: magnification equals image size divided by actual size. If you know any two of the three, the rule gives you the third.
A photo shows a cell 30 mm across, and the real cell is 0.1 mm across. Divide 30 by 0.1 and you get 300, so the image is 300 times life size. The rule also runs backwards: actual size equals image size divided by magnification.
Tiny lengths need tiny units. One millimetre holds 1000 micrometres, and one micrometre holds 1000 nanometres. A mitochondrion image 32 mm across at 8000 times gives 0.004 mm, which is 4 micrometres. A scale bar shows real length: four spans of a 5 micrometre bar mean a 20 micrometre cell. Use a light microscope for living cells, which it keeps alive, and an electron microscope for finer detail when the sample need not stay alive. Always write the unit on your answer.
Read the scale bar before you trust your eyes. A long bar on a highly magnified photo can still mean a tiny cell. Pick a light microscope for living cells, and an electron microscope when the sample need not stay alive.
Divide image by real to get magnification, convert in steps of 1000, and let the scale bar tell you the truth.
The rewritten readings were written for this dataset.
More to read
Choosing a microscope
Microscopy reveals objects beyond unaided vision. In a compound light microscope, an objective and an eyepiece enlarge the view together. Multiply their magnifications to calculate the total: x10 multiplied by x40 gives x400.
Light microscopes allow observation of living cells. However, the wavelength of visible light limits the detail they can distinguish.
Electron microscopes replace light with an electron beam. Its shorter wavelength allows finer resolution and greater useful magnification. These instruments can reveal structures within mitochondria or details on virus surfaces, but specimens generally cannot remain alive.
A scanning probe microscope maps a specimen's surface using a very fine tip. The tip moves across or just above the surface and detects local interactions, somewhat like fingers reading braille.
Match the instrument to the investigation. To follow a living cell as it moves or divides, choose light microscopy. To examine structures much smaller than visible light can resolve, electron microscopy offers finer detail.
What a cell image can reveal
Living organisms consist of cells, usually too small for unaided observation. Microscopes make cell study possible, but image size alone is not enough.
Magnification compares the size of an image with the size of its subject. Resolution determines whether nearby details can be distinguished. Contrast makes structures look different enough to tell apart.
A light microscope directs visible light through a specimen or onto its surface. Glass lenses enlarge the view, showing whole cells and some larger internal structures. Living specimens can be observed this way.
An electron microscope forms images using electrons. Their shorter wavelength supports finer resolution and greater useful magnification, revealing details such as mitochondrial folds.
Microscope observations helped establish cell theory: organisms contain at least one cell; cells are life's basic units; and new cells arise only from existing cells. Continued observation has supported these principles.
Cells and the instruments used to study them
Cells are life's smallest units. Most require a microscope to be seen. Electron microscopy offers finer resolution and greater useful magnification than light microscopy, revealing very small internal structures. Light microscopes are easier to operate and can show living cells.
Cell theory states that organisms contain at least one cell, that cells are the basic units of living things, and that new cells arise only from existing cells.
Different cells, different viewing tools
Cells from a nose lining, an onion and bacteria share basic cell features, although their structures differ. Visible light and glass lenses can produce enlarged views of nose and onion cells. A scanning electron microscope instead scans a specimen with electrons and can reveal bacterial surfaces.
Electron microscopy provides finer detail and greater useful magnification than light microscopy. The best choice depends on the structures you need to examine and whether the specimen must remain alive.
Length review
Length tells you how long something is from one end to the other, and it's how we describe height, width, and distance. The metric system measures length using millimetres, centimetres, metres, and kilometres. These units are all connected by powers of ten, so converting between them is really just moving a decimal point. For example, a door that is about 2 metres tall is the same as 200 centimetres, because there are 100 centimetres in a metre. The same idea works for even smaller units. There are 1000 micrometres in a millimetre, and 1000 nanometres in a micrometre. Every time you move to a smaller unit, you multiply by 1000, and every time you move to a bigger unit, you divide by 1000. Keeping track of that factor of a thousand is the whole trick to converting metric lengths correctly, whether you are measuring a doorway or the width of a cell under a microscope.
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