Magnification Calculations

Magnification

After looking at cells under a microscope, you might be asked to do some calculations. These can seem tricky, but there’s a simple trick to remember how to work them out!

Use the AIM triangle to help you with the three key equations. The triangle looks like this:

  • A stands for Actual Image Size
  • I stands for Image Size
  • M stands for Magnification

How to Use the Triangle

  • To find the Actual Image Size (A): Cover the A and multiply the Image Size (I) by the Magnification (M).
  • To find the Image Size (I): Cover the I and divide the Actual Image Size (A) by the Magnification (M).
  • To find the Magnification (M): Cover the M and divide the Actual Image Size (A) by the Image Size (I).

Just remember: AIM—it’s that easy!

Magnification Triangle
A useful triangle to remember the magnification calculations

Actual image is the real size of the “thing” you are looking at (sometimes called The Object).

Image Size is the measurement, length/height/width, of the image you are looking at.

Magnification is how many times bigger something is being observed compared to its actual size.

When looking at cells we are looking at very small things so you may see some new measurements that you need to understand.

A list of conversions for the length of an object

The common one to remember is that 1mm = 1000µm

Tip: For any problems you get, it usually helps to convert all your units to the same unit first. 

 

Example - Magnification

You are given an image of a cell and you measure the width to be 2mm. You are told that the Actual Image size is 0.02mm so you can now easily work out the magnification using the equation below.

Magnification Equation for Magnification

Since they are already both in the same units you don’t need to convert them and just put them straight into the equation so you have. 

Magnification =  2/0.02 = 100

This means the diagram has been magnified 100 times 

Example - Image Size

This time, you have been told that the actual size of what you are looking at is 400µm wide and that the magnification is x50. 

Magnification Equation for Image Size

We now have everything we need to work out the answer and just need to substitute our values into the equation.

Image Size = 0.4 x 50 = 2,000

So the image size is 20,000µm or 20mm

Example - Actual Size

Here we have an image of a cell. It measures 15mm wide and the magnification is x400.

Magnification Equations for Actual Image

Using the equation we can work out what the real size of the cell is.

Actual Image = 15/400 = 0.0375

So the real cell is 0.0375mm wide. You will want to convert this into µm so just times it by 1000 giving us a width of 37.5µm

Once you can use the equations and convert units with ease you can also use the same process to measure sub-cellular structures in the cells and estimate the surface area etc…