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B1 D) Microscopy: Magnification Calculations
B1 D) Microscopy: Magnification Calculations
Microscopes allows us to look at things that are too small to see with the naked eye, such as cells. Microscopes magnify things – they make objects seem bigger than they are. Microscopes also increase the resolution of what we see – they allow us to see objects in greater detail (resolution is the sharpness of an image; a greater resolution means that it is easier to distinguish different parts/ structures in what we are looking at). Overtime microscopes have developed, which has increased the levels of magnification and resolution. This has allowed scientists to see subcellular structures closer up and in more detail, which has increased our understanding of subcellular structures and how cells work.
There are two microscopes that you need to know about. These are light microscopes and electron microscopes.
There are two microscopes that you need to know about. These are light microscopes and electron microscopes.
- Light microscopes were invented in the 1590s, and they pass light through a specimen. They allowed scientists to see large subcellular structures in cells, such as nuclei and chloroplasts.
- Electron microscopes were invented in the 1930s, and they use electrons (hence the name). They have a higher magnification and resolution than light microscopes. This allowed scientists to see cells closer up and in greater detail. When we look at cells through an electron microscope we can see ribosomes, mitochondria and the formation of the nucleus in more detail.
Magnification Calculations
Magnification refers to how many times bigger the object is when looking through a microscope compared to real life. We can find the magnification of a microscope by dividing the image size by the real size.
Magnification refers to how many times bigger the object is when looking through a microscope compared to real life. We can find the magnification of a microscope by dividing the image size by the real size.
The image size and real size need to be in the same units. If they are not in the same units, we must convert the values so that they are in the same units.
The formula triangle for magnification (m), image size (i) and real size (r) is shown below.
The formula triangle for magnification (m), image size (i) and real size (r) is shown below.
Let’s have some examples.
Example 1
I look at a bacteria cell through a microscope that has a magnification of x100. The length of the bacteria cell in the image produced by the microscope is 4 mm. Find the real length of the bacteria cell. Give your answer in micrometres (μm).
The question is asking us to find the real length of the bacteria. We find the calculation that we need to undertake by covering up the real size (r) in the formula triangle. When we do this, we see that we find the real size by dividing the image size by the magnification.
I look at a bacteria cell through a microscope that has a magnification of x100. The length of the bacteria cell in the image produced by the microscope is 4 mm. Find the real length of the bacteria cell. Give your answer in micrometres (μm).
The question is asking us to find the real length of the bacteria. We find the calculation that we need to undertake by covering up the real size (r) in the formula triangle. When we do this, we see that we find the real size by dividing the image size by the magnification.
The question tells us that the image size is 4 mm and the magnification is 100. We sub these values into the calculation.
The units for the image size and real size will be the same. Therefore, as the units for the image size were mm (millimetres), the units for the real size will also be mm (millimetres).
The question asked us to give our answer in micrometres (μm). 1 mm is 1000 μm, so we convert millimetres (mm) to micrometres (μm) by multiplying by 1000.
The question asked us to give our answer in micrometres (μm). 1 mm is 1000 μm, so we convert millimetres (mm) to micrometres (μm) by multiplying by 1000.
The real length of the bacteria cell is 40 μm.
Example 2
Sometimes we will be given a scale drawing of a specimen from a microscope and the real size of the specimen. We will then be asked to find the magnification of the microscope. We find the magnification by measuring the length of the specimen on the scale drawing (the image size). We then sub the values into the calculation from the formula triangle to find the magnification. Let’s have an example.
Question
A student looked through a microscope and completed a scale drawing, which is shown below.
Sometimes we will be given a scale drawing of a specimen from a microscope and the real size of the specimen. We will then be asked to find the magnification of the microscope. We find the magnification by measuring the length of the specimen on the scale drawing (the image size). We then sub the values into the calculation from the formula triangle to find the magnification. Let’s have an example.
Question
A student looked through a microscope and completed a scale drawing, which is shown below.
Note – these drawing will not be to scale on your internet browser/ computer/ phone screen.
The real length of the cell is 0.013 mm. Find the magnification.
The question is asking us to find the magnification (m). When we cover magnification up in the formula triangle, we see that we find the magnification by dividing the image size by the real size.
The question is asking us to find the magnification (m). When we cover magnification up in the formula triangle, we see that we find the magnification by dividing the image size by the real size.
The question tells us that the real size is 0.013 mm. We are not given the image size, but we can measure the image size on the scale drawing. For magnification calculations, the values for image size and real size must be in the same units. The real size is in millimetres, so the image size must also be in millimetres.
Note – these drawing will not be to scale on your internet browser/ computer/ phone screen.
The image size is 39 mm and the real size is 0.013 mm. These values are in the same units, so we can sub them into the magnification calculation.
The magnification is 3000.
Example 3
We are now going to have a look at an example where the values are in standard form. We answer these questions in exactly the same way; we just need to be careful when we sub the values into the calculation (especially when we are dividing).
Question
We are now going to have a look at an example where the values are in standard form. We answer these questions in exactly the same way; we just need to be careful when we sub the values into the calculation (especially when we are dividing).
Question
A specimen has a width of 4.5 x 10-6 m. The specimen is viewed through a microscope with a magnification of 200. Find the width of the image under the microscope. Give your answer in metres and in standard form.
The question is asking us to find the image size (i). When we cover image size up in the formula triangle, we see that we find the image size by multiplying the magnification by the real size.
The question tells us that the magnification is 200 and the real size is 4.5 x 10-6; we sub these values into the calculation.
The image size is 0.0009 metres. We now need to put this value into standard form. The value of A in standard form must be between 1 and 10 (1 ≤ A < 10). The value of A for 0.0009 would be 9.
The next step is to see how many places we move the decimal point in order to give us 9.
From the diagram above, we can see that we move the decimal point 4 places to the right. Therefore, n is -4. So, 0.0009 in standard form is 9 x 10-4.
The image size is 9 x 10-4 metres.