AS Biology 9700: Magnification, Actual Size and Resolution Calculations

A textbook shows two images produced from electron micrographs taken by a research group studying liver cells.

Image 1 shows a single mitochondrion. In the printed image, the mitochondrion measures 24 mm in length. The image is labelled with a magnification of ×15 000.

Image 2 shows a chloroplast granum from a different, plant cell, included for comparison. In this image, the granum has a width of 3.6 mm, and its actual width is known from other data to be 0.4 μm.

(a) Calculate the actual length of the mitochondrion in Image 1, giving your answer in micrometres (μm). Show your working. [3]

(b) A student claims that this mitochondrion could never be seen using a light microscope. Using the resolution of a light microscope, evaluate whether the student is correct. [2]

Part (a): Actual length of the mitochondrion

The formula linking magnification, image size and actual size is:

magnification = image size ÷ actual size

Rearranging to find the actual size:

actual size = image size ÷ magnification

Before dividing, both quantities must be in the same units. The image size is given in millimetres, so convert it to micrometres, since 1 mm = 1000 μm:

24 mm × 1000 = 24 000 μm

Now divide by the magnification:

24 000 μm ÷ 15 000 = 1.6 μm

So the actual length of the mitochondrion is 1.6 μm.

Part (b): Evaluating the resolution claim

A light microscope has a resolution of roughly 0.2 μm (200 nm). This is the smallest distance between two points that it can distinguish as separate. The mitochondrion’s actual length, calculated in part (a), is 1.6 μm, which is larger than this 0.2 μm resolution limit.

This means the mitochondrion is not too small to be resolved by a light microscope: it is large enough to just be seen as a tiny, distinct structure. The student’s claim that it “could never be seen” is therefore incorrect.

However, this does not mean a light microscope would show it clearly. The mitochondrion’s internal features, such as its double membrane and the folds of the inner membrane (cristae), are separated by distances of only a few tens of nanometres, far below the light microscope’s 0.2 μm resolution limit. Seeing that internal detail requires the much better resolution of an electron microscope.

Part (c): Magnification of the chloroplast granum

Using the same rearranged formula, but now solving for magnification:

magnification = image size ÷ actual size

Convert the image width to the same unit as the actual size (micrometres), since 1 mm = 1000 μm:

3.6 mm × 1000 = 3600 μm

Now divide by the actual width:

3600 μm ÷ 0.4 μm = 9000

So the magnification of the chloroplast granum image is ×9000.

Final answers

(a) Actual length of the mitochondrion = 1.6 μm.
(b) The student is incorrect. At 1.6 μm, the mitochondrion is above the light microscope’s ~0.2 μm resolution limit and could just be seen, though its internal detail could not be resolved without an electron microscope.
(c) Magnification of the chloroplast granum image = ×9000.