0610 · 2.2Size of specimens

Magnification formula and units

0:00Look at a photo of a cell in a textbook and it might be as wide as your thumb. But the real cell is far too small to see with your eyes. So how big is it really? Biologists answer this with one short formula. By the end of this video you will be able to use it in every direction, to find the magnification, the actual size of a specimen, or the size of its image.

0:19You will also learn how to switch between millimetres and micrometres, the tiny unit that cell sizes are usually given in, and you will see the mistakes that lose marks on these questions. You need two things before we start. The first is the word specimen. A specimen is simply the thing you are looking at, such as a cell, an insect or a leaf. The second is the millimetre.

0:39There are 10 millimetres in a centimetre, and in this topic every length you measure with a ruler should be in millimetres. When you look at a specimen through a microscope, or at a photo or a drawing of it, you are looking at an image. The image is bigger than the real thing. Magnification tells you how many times bigger the image is than the actual specimen. Here is the idea in a simple case.

1:00Imagine an ant that is 5 millimetres long. You draw it 50 millimetres long. Your drawing is 10 times as long as the real ant, so the magnification is 10. You found that by dividing 50 by 5. That is the whole formula. Magnification equals image size divided by actual size. The image size is how big the specimen appears in the drawing or the photo. The actual size is how big the specimen really is.

1:24You can rearrange the formula to find any one of the three quantities. Actual size equals image size divided by magnification. And image size equals magnification multiplied by actual size. A formula triangle can help you remember this. Write image size at the top, and magnification and actual size along the bottom. Cover the quantity you want, and the other two show you what to do. If they sit side by side, multiply them.

1:48If one is above the other, divide. Two rules make every one of these calculations work. First, the image size and the actual size must be in the same unit. If one is in millimetres and the other is in micrometres, you must convert one of them first. Second, magnification has no unit. It is just a number of times. You write it with a multiplication sign in front of the number, which we read as times.

2:10So a magnification of 10 is written as times 10, and never as 10 millimetres.

Calculating magnification

2:15Let us work through an example. A photo shows a plant cell. On the photo, the cell is 40 millimetres long. Its actual length is 0.05 millimetres. Calculate the magnification. Step one, check the units. Both are in millimetres, so we can carry straight on. Step two, write down the formula. Magnification equals image size divided by actual size. Step three, put in the numbers. Magnification equals 40 divided by 0.05, which is 800.

2:43So the magnification is times 800. Always check that your answer makes sense. The photo is much bigger than the real cell, so the magnification should be a big number, bigger than 1. If you had divided the other way, 0.05 divided by 40, you would get a tiny number. That would mean the photo was smaller than the cell, which cannot be right, so you would know to turn the division around.

Finding actual and image size

3:05In many exam questions, you have to measure the image yourself. Here is an example. A question shows a drawing of a flea, and says the drawing is magnified times 20. You are asked to find the actual length of the flea. First, measure the drawing with a ruler, from the very front of the head to the very back of the body, along the longest line. Line up the zero on your ruler with one end, and measure in millimetres, not centimetres.

3:29Say the drawing measures 30 millimetres. Now choose the right arrangement of the formula. We want the actual size, so actual size equals image size divided by magnification. That is 30 divided by 20, which is 1.5. So the flea is 1.5 millimetres long. Notice that this answer has a unit, millimetres, because it is a length. Magnification has no unit, but sizes always do. A third type of question asks for the image size.

3:56A pollen grain is 0.04 millimetres wide. It is viewed at a magnification of times 500. How wide does it appear in the image? Image size equals magnification multiplied by actual size. That is 500 multiplied by 0.04, which is 20. So the image is 20 millimetres wide. The same formula works for a drawing you make yourself in a practical. The image size is then the length of your own drawing, measured with a ruler, and the actual size is the length of the real specimen.

Micrometres and scale bars

4:26Cells are so small that millimetres give awkward numbers like 0.05 or 0.04. So biologists often use a much smaller unit called the micrometre. Its symbol is the Greek letter mu followed by the letter m. One micrometre is one thousandth of a millimetre. That means there are 1000 micrometres in one millimetre. Converting is just multiplying or dividing by 1000. To change millimetres into micrometres, multiply by 1000. To change micrometres into millimetres, divide by 1000.

4:57Here is a way to check which one to do. Micrometres are smaller units, so you need more of them to measure the same length. When you go from millimetres to micrometres, the number must get bigger. Let us try it. The plant cell in the first example was 0.05 millimetres long. Multiply by 1000, and that is 50 micrometres. The pollen grain was 0.04 millimetres wide, which is 40 micrometres.

5:21Those are much easier numbers to read and compare. Now a harder example that mixes units. On a photo, a bacterium is 12 millimetres long. Its actual length is 2 micrometres. Calculate the magnification. The trap is that the two sizes are in different units, so we convert first. Let us change the actual size into millimetres. 2 micrometres divided by 1000 is 0.002 millimetres. Now, magnification equals image size divided by actual size, which is 12 divided by 0.002.

5:53That gives 6000. So the magnification is times 6000. You could just as well convert the image size into micrometres instead. 12 millimetres multiplied by 1000 is 12000 micrometres. Then 12000 divided by 2 is 6000, the same answer. It does not matter which one you convert, as long as both sizes end up in the same unit. Here is one where the answer has to be in micrometres. A photo of a cheek cell is magnified times 1500, and on the photo the cell measures 90 millimetres across.

6:24Give its actual size in micrometres. Actual size equals image size divided by magnification, so 90 divided by 1500 is 0.06 millimetres. The question wants micrometres, so multiply by 1000. The cheek cell is 60 micrometres across. Some photos come with a scale bar instead of a magnification. A scale bar is a short line drawn on the photo, labelled with the actual length it stands for. You can use it to work out the magnification.

6:50Say the scale bar is labelled 10 micrometres, and when you measure it on the page with a ruler it is 20 millimetres long. The bar on the page is the image size, 20 millimetres, and its label is the actual size, 10 micrometres. Convert the label into millimetres first. 10 micrometres divided by 1000 is 0.01 millimetres. Then magnification equals 20 divided by 0.01, which is 2000. So the photo is magnified times 2000.

Common mistakes and recap

7:16Let us collect the mistakes that lose marks. The first is mixing units. If you divide 12 millimetres by 2 micrometres without converting, you get 6, which is a thousand times too small. Always check that both sizes are in the same unit before you divide. The second is dividing the wrong way round. Magnification is image size divided by actual size. A quick check is that a magnified image always gives a magnification bigger than 1.

7:42The third is putting a unit on the magnification. Write times 6000, never 6000 millimetres. The fourth is measuring in centimetres. If your ruler shows 3 centimetres, that is 30 millimetres. Using 3 instead of 30 makes your answer 10 times too small. And the fifth is converting the wrong way. Going from millimetres to micrometres, the number gets bigger, so you multiply by 1000. Going from micrometres to millimetres, the number gets smaller, so you divide by 1000.

8:10In the exam, these questions often come with a drawing or a photo, and a length for you to measure. Show every step of your working: your measurement, the formula, the numbers and the answer with its unit. Even if you make a slip in the arithmetic, you can still earn marks for the method. And give a sensible answer, not every digit from your calculator. Let us recap. Magnification equals image size divided by actual size.

8:34Rearranged, actual size equals image size divided by magnification, and image size equals magnification multiplied by actual size. Both sizes must be in the same unit, and magnification has no unit. It is written as times a number. Measure images with a ruler in millimetres. There are 1000 micrometres in a millimetre, so multiply by 1000 to go from millimetres to micrometres, and divide by 1000 to go back. And always check that your answer makes sense.

9:01A magnified image means a magnification bigger than 1, and an actual size much smaller than the image.