Magnification vs Resolution Calculations

0:39Magnification formula

Start with magnification. It tells you how many times larger the image is than the real object. The formula is magnification equals image size divided by real size. Put it in a triangle. Image on top, actual size and magnification along the bottom. Cover up the one you want. There is one rule that loses more marks than any other. Both sizes must be in the same units before you divide.

1:07Converting units

To go from millimetres to micrometres, multiply by one thousand. Say the image in a drawing is forty five millimetres long, and the real cell is thirty micrometres. Forty five millimetres is forty five thousand micrometres. Divide forty five thousand by thirty, and the magnification is one thousand five hundred.

The same triangle works backwards. Cover actual size, and it is image divided by magnification. Suppose an image is twelve millimetres long, at a magnification of four hundred. Twelve millimetres is twelve thousand micrometres. Divide by four hundred, and the real object is thirty micrometres. Same units first, every single time.

1:53Resolution

Now resolution. It is the ability to see two points that are close together as separate points. If they merge into one blob, the microscope has not resolved them. So resolution is about detail and clarity. Magnification is only about size. A light microscope has a limited resolution, so past a certain point, enlarging the image only gives you a bigger blur.

You can enlarge a blurry image as much as you like, but you will not see any new detail. So higher magnification does not always mean a clearer image.

2:29Graticule and stage micrometer

Now measuring under a light microscope. There are two scales. The eyepiece graticule sits inside the eyepiece. It is a ruler with divisions, but those divisions have no fixed size. The stage micrometer is a slide with a ruler etched on it. Its divisions have a known length, here ten micrometres each. And a graticule changes value every time you change the objective lens, so you must calibrate it at each magnification.

2:58Calibrating the graticule

To calibrate, line up the two scales and find where the lines match. In our question, eighty graticule divisions match twenty stage divisions. Twenty divisions of ten micrometres is two hundred micrometres. So eighty graticule divisions cover two hundred micrometres.

Divide two hundred by eighty. One graticule division is two point five micrometres.

3:24Measuring the cell

Now measure the cell. It is fourteen graticule divisions long. Fourteen times two point five gives thirty five micrometres. Do not forget the unit. A number with no unit loses the mark. And check it makes sense. A typical animal cell is tens of micrometres across, so thirty five fits.

If you got thirty five thousand, you have slipped a unit somewhere.

4:20Examiner trap and recap

The trap. Never say a higher magnification gives a clearer image. Clarity is resolution. Size is magnification.

Recap. Calibrate the graticule against the stage micrometer, convert to the same units, then use image over actual size.

Next time, we separate cell parts by cell fractionation and ultracentrifugation.