Microscopy and the magnification equation

How did anyone first see a ribosome, the cell's tiny protein-maker? No ordinary light microscope can show one, however good its lenses. The obvious fix is a stronger lens and a bigger picture, but a bigger picture was never what was missing. The microscope that first showed one used no light at all. This video is about what it had that the old brass ones never did. The first ribosome view gets its answer once we know how fine a detail a microscope can show.

Start with the ordinary light microscope, the kind in a school lab. At the bottom, a lamp shines light upwards. The light passes up through the stage, the flat platform that holds the specimen. The specimen sits on a slide, a strip of glass, under a cover slip, a thin square of glass that keeps it flat. Above it, the lenses bend that light to make an enlarged image for your eye. Onion skin looks almost see-through. Which helps: more light, a stain, or a thicker slice? A stain. A stain is a coloured dye that makes a colourless specimen visible, or picks out one structure, such as the nucleus.

Two words carry this topic, and they mean different things. Magnification is how many times bigger the image is than the real object. Resolution is the smallest gap between two points that still shows as a gap. A microscope with higher resolution shows two points as separate even when they are very close together, so it shows finer detail. A light microscope image is blown up on a huge screen. Does any new detail appear? No. Only the magnification goes up. The resolution is fixed by the microscope, so the blur gets bigger too. So magnification is how big; resolution is how much detail. Stretching a photo on your phone with two fingers does the same thing: past a point it gets bigger, and no new detail appears. An electron microscope uses a beam of electrons instead of light. It has a much higher magnification and a much higher resolution, so it shows sub-cellular structures a light microscope cannot, such as ribosomes and the inside of a mitochondrion. That is how a ribosome was first seen, in the nineteen-fifties: not just a bigger picture, but a far higher resolution. Seeing structures like that in detail is how biologists came to understand what each sub-cellular structure does. Say electron microscope in full, every time. An electron microscope picture has no true colour, which helps you name the instrument from the image alone. One examiner's report on a Foundation paper says the least successful answers confused the electron and light microscopes, or said electronic microscope. In plain words, some students named the wrong microscope, and some named the right one with the wrong word. The fix: write electron, after the particle, and never electronic.

Now two students' answers about what an electron microscope does better. One writes, you can zoom in more. The other writes, you can see the structures more clearly. Both are marked wrong, and the job is to say why. Why does neither of those answers score? Both are too vague to earn the mark. Neither says what the electron microscope really gives you: more magnification, higher resolution, or more detail. Now match each answer to magnification or resolution: which was each student reaching for? The first student, zoom in more, was reaching for higher magnification. The second student was reaching for higher resolution. A full answer says both: higher magnification and higher resolution. A second examiner's report, from another Foundation paper, says there were many references to both microscopes being able to see structures more clearly, and being able to zoom in. Neither point gained credit. The same report says the most common creditworthy answer for an electron microscope was being able to see structures in more detail, followed by greater magnification or higher resolution. In plain words, the two everyday phrases scored nothing, while more detail, higher magnification and higher resolution did. Swap the everyday phrase for the technical word. Write higher magnification, or higher resolution, or better still, both.

Resolution also decides what goes in a drawing. Under a light microscope, a cheek cell shows its outline, its nucleus and its cytoplasm, and not much more. A drawing from a light microscope therefore shows only what you can see down it. And every biological drawing carries its magnification, written underneath. Now try one: should a light microscope drawing of a cheek cell show its ribosomes? No. Ribosomes are too small for a light microscope to resolve, so they could not have been seen. A third examiner's report, on a Foundation drawing question, says the most common answer that scored nothing wanted more detail added to the drawing, with labelled sub-cellular structures such as mitochondria and ribosomes, which would not be visible. The same report says very few students know that the drawing should have the magnification added. Those students drew what they could not have seen, and left off the magnification. Both halves are fixed the same way: draw only what you can see, and write the magnification under the drawing.

Now the one equation in this topic. Magnification equals image size divided by real size. Image size is how big the thing looks in the photo or the drawing. Real size is how big the object really is. Magnification has no unit, because it is a length divided by a length, so the units cancel. Here it is on small numbers first. A drawing ten millimetres long of a thing one millimetre long is ten times bigger. Ten divided by one is ten, so the magnification is times ten. The same three numbers give the other two forms. Image size equals magnification times real size, and ten times one gives back the ten. Real size equals image size divided by magnification, and ten divided by ten gives back the one. Whichever two you are given, you can find the third. One rule keeps it right: both lengths in the same unit, on their own line, before anything goes into the equation. Here is a photo of a mitochondrion, forty-two millimetres long, measured end to end across one whole mitochondrion. The label says times fifteen thousand, and the real length is wanted in micrometres. Which form of the equation do you need for the real size? Real size equals image size divided by magnification, because the real size is the unknown. Then the unit line. The answer is wanted in micrometres, so the image size goes into micrometres first. Remember, millimetres to micrometres is one rung down the unit ladder, so times a thousand. Forty-two times a thousand is forty-two thousand micrometres. Image size, forty-two thousand micrometres. Real size, the unknown, in micrometres. Same unit, yes. Now substitute. Real size equals forty-two thousand micrometres divided by fifteen thousand. The thousands cancel, so that is forty-two divided by fifteen. Forty-two divided by fifteen is two point eight, because fifteen times two point eight is forty-two. That makes the real length two point eight micrometres. And that is believable, because a mitochondrion is about one to a few micrometres long. Forgetting to convert would have meant forty-two divided by fifteen thousand. That gives nought point nought nought two eight, and no mitochondrion is that small in micrometres.

Now a different one, built the other way round. A drawing of a chloroplast is four centimetres long, and the real chloroplast is five micrometres long. A student divides four by five and gets a magnification of nought point eight. That cannot be right, and a quick sense check shows it. What has gone wrong with four divided by five? The units. Four is in centimetres and five is in micrometres, so they cannot be divided as they stand. A magnification under one would mean a drawing smaller than the chloroplast itself. Fix the units first, on their own line. Centimetres to millimetres is times ten, the one step here that is ten and not a thousand. Four times ten is forty millimetres. Then millimetres to micrometres is one rung down the ladder, so times a thousand. Forty times a thousand is forty thousand micrometres. Image size, forty thousand micrometres. Real size, five micrometres. Same unit, yes, so now the magnification is image size divided by real size. Now finish it: what is forty thousand divided by five, as a magnification? Times eight thousand. Forty thousand divided by five is eight thousand. A magnification carries no unit, so the answer is times eight thousand with nothing after it. A photomicrograph is a photo taken down a microscope. One examiner's report on a Higher paper describes a question where students measured a bacterium cell on one. It says some measured two cells rather than one. The same report says most students put their answer into standard form correctly, although a few measured in centimetres and so were out by an order of magnitude. In plain words, measuring two cells doubles the image size. And centimetres in place of millimetres puts the answer out by a factor of ten, which is one order of magnitude. Two checks fix both slips. Measure one whole structure, edge to edge. Then write the unit line before you substitute.

This next part is calculating with numbers in standard form. On some boards it is on both Foundation and Higher papers; on others it is marked Higher only. Either way, nobody needs to stop here. A bacterium is two point nought times ten to the minus six metres long. A ribosome is two point five times ten to the minus eight metres across. Line up the powers of ten, one above the other, before any arithmetic. Compare the powers alone first: how many times longer does that make the bacterium? A hundred times, to start with. Ten to the minus six is bigger than ten to the minus eight, by two steps. Each step is a factor of ten, so two steps is ten times ten, which is a hundred. Now the numbers in front. The bacterium has two point nought where the ribosome has two point five. Two divided by two point five is nought point eight, because two point five times nought point eight is two. The numbers in front shrink the hundred a little. A hundred times nought point eight is eighty. The bacterium is eighty times longer than the ribosome. Last, give the answer in the form the question asks for, whether that is standard form, a number of significant figures, or a named unit. Read the question again before you write the final line. Now one for you: the chloroplast's five micrometres, in metres in standard form? Five times ten to the minus six metres. Micro means ten to the minus six, and five already has one digit before its point. The chloroplast is smaller than a metre, so the negative power checks out.

Before the questions, the equation once more: magnification equals image size divided by real size, with both lengths in one unit. Then three questions, two of them on numbers this video has not used. A three-micrometre cell is sixty millimetres long in a photo. What is the magnification? Times twenty thousand. Sixty millimetres is sixty thousand micrometres. Sixty thousand divided by three is twenty thousand. Here's a different kind: what two things does an electron microscope do better? Higher magnification and higher resolution, and it is that higher resolution the old brass microscopes never had. That is how the first ribosome was seen. Is four times ten to the minus seven metres longer than three times ten to the minus six? No. Minus six is one step above minus seven, which is a factor of ten. Then three divided by four is nought point seven five, and ten times that is seven and a half. That makes three times ten to the minus six seven and a half times longer.

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That completes our chapter on Cells and microscopy. Next chapter: Cell division, specialisation and stem cells. Hopefully that's next in your feed, but if not, search for ScholaFly B I oh two, oh oh.

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