Microscopy

AQA·Biology (Combined Science)·4.1.1.5·Trilogy — Higher

Light and electron microscopy

Light microscopes and electron microscopes allow biologists to see cells, but they differ greatly in the detail they can reveal. Electron microscopy was developed after light microscopy and offers much higher magnification and resolving power.

Magnification describes how much larger the image is than the object. Higher magnification produces a larger image, but a larger image does not necessarily show more detail.

Resolution is the ability to distinguish two points that are close together as separate. If a microscope cannot resolve two nearby points, they appear blurred together, even when the image is magnified.

Electron microscopes have greater resolving power than light microscopes, so they can distinguish points that are much closer together. This allows cells to be seen in much finer detail and has enabled biologists to observe and understand many more sub-cellular structures: structures within cells.

Microscope magnification and resolution

A microscope produces an image of an object. Magnification tells us how many times larger the image is than the real object. It compares a length on the image with the corresponding real length.

magnification=size of imagesize of real object\text{magnification} = \frac{\text{size of image}}{\text{size of real object}}

The image size and real size must be expressed in the same units before calculating the ratio. Magnification itself has no units: a magnification of $$\times 400$$ means that each measured length on the image is 400 times the corresponding real length.

Calculating image size and real size

For an object viewed with an optical microscope, measure a length on its image and divide by the magnification to find the corresponding real length. The same relationship can be rearranged to find image size.

real size=image sizemagnificationimage size=real size×magnification\begin{aligned} \text{real size} &= \frac{\text{image size}}{\text{magnification}} \\ \text{image size} &= \text{real size} \times \text{magnification} \end{aligned}

For example, if an image is $$20\ \text{mm}$$ long at a magnification of $$\times 400$$, the real object is $$20\ \text{mm} \div 400 = 0.05\ \text{mm}$$ long. This is also $$50\ \mu\text{m}$$.

Resolution and visible detail

Resolution is the ability to distinguish two close points as separate. A microscope with a smaller minimum distinguishable distance has better resolution: it can distinguish points that are closer together.

Magnification makes an image larger, but resolution determines how much detail can be distinguished. Enlarging an image beyond its resolution limit makes the existing image bigger without revealing additional detail.

Cell size and orders of magnitude

Cell dimensions are very small lengths, so they are often measured in micrometres or nanometres rather than metres. To compare two sizes reliably, first express them in the same unit.

The relationships between these units and the metre are:

1 mm=10−3 m,1 μm=10−6 m,1 nm=10−9 m1\,\mathrm{mm}=10^{-3}\,\mathrm{m},\qquad 1\,\mathrm{\mu m}=10^{-6}\,\mathrm{m},\qquad 1\,\mathrm{nm}=10^{-9}\,\mathrm{m}

A millimetre contains $$1000,\mathrm{\mu m}$$, and a micrometre contains $$1000,\mathrm{nm}$$. For example, $$0.01,\mathrm{mm}$$ is the same length as $$10,\mathrm{\mu m}$$.

Standard form for cell sizes

Standard form expresses a positive measurement as $$a\times10^n$$, where $$1\leq a<10$$ and $$n$$ is an integer. For example, $$0.000009,\mathrm{m}$$ is $$9\times10^{-6},\mathrm{m}$$.

A negative power of ten represents a fraction of a unit: $$10^{-6}$$ means one millionth. The negative exponent does not mean that the length itself is negative.

Comparing cell sizes

A ratio tells us how many times larger one linear dimension is than another. Convert the measurements to the same unit, then divide the larger size by the smaller size. For measurements in standard form, divide the coefficients and subtract the exponents:

a×10mb×10n=ab×10m−n\frac{a\times10^m}{b\times10^n}=\frac{a}{b}\times10^{m-n}

For example, compare a cell dimension of $$9,\mathrm{\mu m}$$ with one of $$100,\mathrm{nm}$$. In metres, these are $$9\times10^{-6},\mathrm{m}$$ and $$1\times10^{-7},\mathrm{m}$$. Their ratio is:

9×10−61×10−7=9×101=90\frac{9\times10^{-6}}{1\times10^{-7}}=9\times10^1=90

The first dimension is therefore 90 times the second. This ratio compares lengths, not areas or volumes.

Orders of magnitude

An order of magnitude is a factor of ten. A ratio of exactly $$10^k$$ represents a difference of $$k$$ orders of magnitude. For an approximate comparison, express the ratio as an approximate power of ten.

In the example, $$90$$ is approximately $$10^2$$, so the dimensions differ by approximately two orders of magnitude. The coefficients matter: comparing only the exponents in $$9\times10^{-6}$$ and $$1\times10^{-7}$$ would miss the factor of $$9$$.

An additive difference and a ratio answer different questions. The two dimensions differ by $$8.9,\mathrm{\mu m}$$, but their multiplicative difference in scale is a factor of $$90$$.