Chapter 2 of 8

All 8 chapters
  1. 1Cell structure in detail, readunderstood
  2. 2Microscopes and size, readunderstood
  3. 3Diffusion, osmosis and active transport, readunderstood
  4. 4Cell division, readunderstood
  5. 5Enzymes, readunderstood
  6. 6Photosynthesis, readunderstood
  7. 7Testing photosynthesis, readunderstood
  8. 8Respiration, readunderstood

S4.1.2 Chapter 2

Microscopes and size

A cell is too small to see. How do scientists know how big it really is?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Calculate magnification from image size and real size
  • Convert between millimetres, micrometres and nanometres

The smallest thing you can see with your eyes alone is about a tenth of a millimetre across. Most cells are much smaller. We need a microscope to see them.

A light microscope shines light through a thin slide. Two lenses magnify what the light shows. The objective lens is close to the slide. The eyepiece lens is the one you look through.

A light microscope from the side. The labels are eyepiece lens, objective lens, slide, stage, light source, coarse focus knob and fine focus knob.eyepiecelensobjectivelensslidestagelightsourcecoarsefocusknobfinefocusknob
Light from below passes through the slide. You turn the coarse knob first to find the picture, then the fine knob to make it sharp.

Each lens has its own magnification. The total magnification is the two multiplied together. An eyepiece of ×10 with an objective of ×40 gives ×400.

Worked example

A microscope has an eyepiece lens of ×10 and an objective lens of ×40. What is the total magnification?

  1. Total magnification = eyepiece magnification × objective magnification.
  2. 10 × 40 = 400.

Answer: ×400

Magnification says how many times bigger the image is than the real object. The rule has three forms, and all of them need the two sizes in the same unit.

Draw it first

The same cell at three magnifications

  1. Three pictures, one after another, of a cell 20 µm wide and its image. At magnification ×2 the image is 40 µm. At magnification ×5 the image is 100 µm. At magnification ×50 the image is 1 mm and the picture says not to scale. Each picture is labelled real size, image size and its magnification.20 µmreal size40 µmimage sizemagnification ×2

    1 At ×2 the image is 2 times the real size: 20 µm becomes 40 µm.

  2. Three pictures, one after another, of a cell 20 µm wide and its image. At magnification ×2 the image is 40 µm. At magnification ×5 the image is 100 µm. At magnification ×50 the image is 1 mm and the picture says not to scale. Each picture is labelled real size, image size and its magnification.20 µmreal size100 µmimage sizemagnification ×5

    2 At ×5 the image is 5 times as wide: 20 µm becomes 100 µm.

  3. Three pictures, one after another, of a cell 20 µm wide and its image. At magnification ×2 the image is 40 µm. At magnification ×5 the image is 100 µm. At magnification ×50 the image is 1 mm and the picture says not to scale. Each picture is labelled real size, image size and its magnification.20 µmreal size1 mmimage sizemagnification ×50not to scale

    3 At ×50 the image is 1 000 µm, which is 1 mm. It is too big to draw to scale here.

Image size = real size × magnification. Turn it round and you get the other two forms. Magnification = image size ÷ real size. Real size = image size ÷ magnification.

Cells are measured in micrometres. One micrometre, written µm, is one thousandth of a millimetre. Things smaller than that, such as ribosomes, are measured in nanometres, written nm. One nanometre is one thousandth of a micrometre.

Three boxes in a column: millimetre (mm), micrometre (µm) and nanometre (nm). Going down each step is × 1 000. Going up each step is ÷ 1 000.millimetre(mm)× 1 000÷ 1 000micrometre(µm)× 1 000÷ 1 000nanometre(nm)
Down to a smaller unit, multiply by 1 000. Up to a bigger unit, divide by 1 000. Two steps down is × 1 000 000: 1 mm = 1 000 000 nm.
A table of sizes with the columns Thing, µm and nm. Ribosome: 0.025 µm, 25 nm. Bacterium: 2 µm, 2 000 nm. Blood cell: 7 µm, 7 000 nm. Plant cell: 40 µm, 40 000 nm.Thingµmnmribosome0.02525bacterium22 000blood cell77 000plant cell4040 000
The same sizes in two units. A blood cell here is a red blood cell, about 7 µm across. These are typical sizes.

Worked example

A cell is 60 µm long. In a drawing it is 12 mm long. What is the magnification?

  1. Change 12 mm to µm. 1 mm = 1 000 µm, so 12 mm = 12 000 µm.
  2. Magnification = image size ÷ real size.
  3. 12 000 ÷ 60 = 200.

Answer: ×200

A cell and its image with the labels 60 µm, 12 mm, real size, image size, magnification ×200 and not to scale. The real size is 60 µm and the image size is 12 mm.60 µmreal size12 mmimage sizemagnification ×200not to scale
The worked example as a picture. Both sizes must be in the same unit before you divide.

Now the limit. A light microscope can magnify up to about ×1 500. It cannot show things smaller than about 0.2 µm, so it cannot show ribosomes. An electron microscope uses a beam of electrons, not light. It magnifies far more and shows ribosomes and the inside of mitochondria.

The difference is resolution. This is how close two points can be and still be seen as two. An electron microscope has a much better resolution. A light microscope can look at living cells. An electron microscope looks at specimens that are no longer alive.

Worked example

An electron micrograph shows a ribosome 5 mm across at a magnification of ×200 000. How many nm across is a ribosome?

  1. Real size = image size ÷ magnification.
  2. Change the image to nm. 1 mm = 1 000 000 nm, so 5 mm = 5 000 000 nm.
  3. 5 000 000 ÷ 200 000 = 25.
  4. A ribosome is 25 nm across.

Answer: 25 nm

A table with the columns Image, Times and Real. The image is 5 mm, the magnification is ×200 000 and the real size is 25 nm.ImageTimesReal5 mm×200 00025 nm
The ribosome example as a table. A 5 mm image at this magnification shows a ribosome 25 nm across.

Try it

Find the magnification of your own drawing

You need: a grain of rice, a lentil or a small seed, a ruler with millimetres, paper and a pencil.

  1. Measure the length of the grain in mm. This is the real size.
  2. Draw the grain on the paper as large as you can, with the same shape.
  3. Measure the length of your drawing in mm. This is the image size.
  4. Divide the image size by the real size.

What you will see: A grain 6 mm long drawn 48 mm long gives 48 ÷ 6 = 8. The drawing is ×8. Scientists write the magnification beside every drawing they make.

If you cannot try it, this is what happens.
A table with the columns Real, Image and Magnification. The real size is 6 mm, the image size is 48 mm and the magnification is ×8.RealImageMagnification6 mm48 mm×8

A wrong idea many people have

A higher magnification always lets us see smaller things.

Why it feels right: If a lens makes things bigger, more of it should show smaller things.

The test that breaks it: Enlarge a photocopy of a printed letter again and again. The edges only get blurry. No new detail appears.

What is true: There is a limit called resolution. Past about ×1 500 a light microscope only makes a bigger blur. To see more detail you need a microscope with a better resolution, such as an electron microscope.

Key words

magnification
how many times bigger an image is than the real object.
eyepiece lens
the lens of a microscope that you look through.
objective lens
the lens of a microscope that is close to the slide.
micrometre
one thousandth of a millimetre, written µm.
nanometre
one thousandth of a micrometre, written nm.
resolution
how close two points can be and still be seen as two.
electron microscope
a microscope that uses a beam of electrons and shows much more detail.

Back to your guess

The answer is C: They divide the size of the picture by the magnification.

The picture is bigger than the cell by the magnification. To get back to the real size, divide the size of the picture by the magnification.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. A cell is 25 µm long. In a drawing it is 5 mm long. What is the magnification?

    Tap your answer.

    1. Yes, that is right. 5 mm = 5 000 µm. 5 000 ÷ 25 = 200.

    2. Not this one. You multiplied 5 and 25. Magnification is image size divided by real size. Try another.

    3. Not this one. You divided 5 by 25 without changing the units. The mm must become µm first: 5 mm = 5 000 µm. Try another.

    See the answer

    ×200

    5 mm = 5 000 µm. 5 000 ÷ 25 = 200.

    • If you chose B: You multiplied 5 and 25. Magnification is image size divided by real size.
    • If you chose C: You divided 5 by 25 without changing the units. The mm must become µm first: 5 mm = 5 000 µm.

  2. A bacterium is 2 µm wide. How wide is that in nm?

    Tap your answer.

    1. Not this one. You divided by 1 000. Going to a smaller unit makes the number bigger, so multiply. Try another.

    2. Not this one. There are 1 000 nm in 1 µm, not 100. Try another.

    3. Yes, that is right. 1 µm = 1 000 nm, so 2 µm = 2 × 1 000 = 2 000 nm.

    See the answer

    2 000 nm

    1 µm = 1 000 nm, so 2 µm = 2 × 1 000 = 2 000 nm.

    • If you chose A: You divided by 1 000. Going to a smaller unit makes the number bigger, so multiply.
    • If you chose B: There are 1 000 nm in 1 µm, not 100.

  3. The image of a cell is 1 mm long at a magnification of ×40. How long is the cell?

    A cell and its image with the labels ?, 1 mm, real size, image size, magnification ×40 and not to scale. The real size is hidden by a question mark. The image size is 1 mm.?real size1 mmimage sizemagnification ×40not to scale
    Tap your answer.

    1. Not this one. 1 ÷ 40 = 0.025, but that answer is in mm, not µm. 0.025 mm is 25 µm. Change the image to µm first: 1 000 ÷ 40 = 25. Try another.

    2. Yes, that is right. Real size = image size ÷ magnification. 1 mm = 1 000 µm, and 1 000 ÷ 40 = 25.

    3. Not this one. You multiplied by the magnification. The cell is smaller than its image, so divide. Try another.

    See the answer

    25 µm

    Real size = image size ÷ magnification. 1 mm = 1 000 µm, and 1 000 ÷ 40 = 25.

    • If you chose A: 1 ÷ 40 = 0.025, but that answer is in mm, not µm. 0.025 mm is 25 µm. Change the image to µm first: 1 000 ÷ 40 = 25.
    • If you chose C: You multiplied by the magnification. The cell is smaller than its image, so divide.

  4. Which of these is the smallest?

    Tap your answer.

    1. Not this one. 0.002 mm is 2 µm, which is 2 000 nm. It is the largest of the three. Try another.

    2. Yes, that is right. In nm the three sizes are 2 000, 500 and 1 000. The smallest is 500 nm.

    3. Not this one. 1 µm is 1 000 nm, which is twice 500 nm. Try another.

    See the answer

    500 nm

    In nm the three sizes are 2 000, 500 and 1 000. The smallest is 500 nm.

    • If you chose A: 0.002 mm is 2 µm, which is 2 000 nm. It is the largest of the three.
    • If you chose C: 1 µm is 1 000 nm, which is twice 500 nm.

  5. Why can an electron microscope show ribosomes when a light microscope cannot?

    Tap your answer.

    1. Yes, that is right. Ribosomes are about 25 nm, much smaller than the 0.2 µm a light microscope can separate. An electron beam can separate points far closer.

    2. Not this one. The limit is not the amount of light. It is the resolution, which an electron beam improves. Try another.

    3. Not this one. Past its limit a light microscope only gives a bigger blur. Resolution, not magnification, is the limit. Try another.

    See the answer

    It has a better resolution, as well as a higher magnification.

    Ribosomes are about 25 nm, much smaller than the 0.2 µm a light microscope can separate. An electron beam can separate points far closer.

    • If you chose B: The limit is not the amount of light. It is the resolution, which an electron beam improves.
    • If you chose C: Past its limit a light microscope only gives a bigger blur. Resolution, not magnification, is the limit.

  6. Which rule gives the magnification of an image?

    Tap your answer.

    1. Not this one. That turns the rule upside down. It gives a number below 1 for a magnified image. Try another.

    2. Not this one. Multiplying the two sizes does not give a magnification. Magnification compares them by dividing. Try another.

    3. Yes, that is right. Magnification says how many times bigger the image is than the real object, so divide the image by the real size.

    See the answer

    image size ÷ real size

    Magnification says how many times bigger the image is than the real object, so divide the image by the real size.

    • If you chose A: That turns the rule upside down. It gives a number below 1 for a magnified image.
    • If you chose B: Multiplying the two sizes does not give a magnification. Magnification compares them by dividing.

  7. From an earlier chapter

    A cell has no nucleus and a cell wall that is not made of cellulose. What kind of cell is it?

    Tap your answer.

    1. Yes, that is right. A bacterium has no nucleus, and its cell wall is not cellulose.

    2. Not this one. A plant cell has a nucleus and a wall of cellulose. Go to S4.1.1. Try another.

    3. Not this one. An animal cell has a nucleus and no cell wall. Go to S4.1.1. Try another.

    See the answer

    A bacterial cell

    A bacterium has no nucleus, and its cell wall is not cellulose.

    • If you chose B: A plant cell has a nucleus and a wall of cellulose. Go to S4.1.1.
    • If you chose C: An animal cell has a nucleus and no cell wall. Go to S4.1.1.

  8. A cell is 40 µm long. In a drawing it is 20 mm long. What is the magnification?

    See the answer

    ×500

    20 mm = 20 000 µm. 20 000 ÷ 40 = 500.

  9. A photograph of a cell is 18 mm long and the magnification is ×300. How long is the real cell in µm?

    A cell and its image with the labels ?, 18 mm, real size, image size, magnification ×300 and not to scale. The real size is hidden by a question mark. The image size is 18 mm.?real size18 mmimage sizemagnification ×300not to scale
    See the answer

    60 µm

    18 mm = 18 000 µm. 18 000 ÷ 300 = 60 µm.

Keep it

Copy this into your exercise book.

Magnification = image size ÷ real size, in the same unit. 1 mm = 1 000 µm. 1 µm = 1 000 nm. Light microscope: up to about ×1 500, cannot show ribosomes. Electron microscope: better resolution.

Draw: A cell and its drawing, with the real size, the image size and the magnification written beside them.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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