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Organisation of the Organism - Size of specimens (Magnification)

Grade 12A LevelBiology

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Magnification is defined as the number of times larger an image is compared to the actual size of the specimen.

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The 'IAM' triangle is the primary tool for calculations: II represents Image size (measured with a ruler), AA represents Actual size of the specimen, and MM represents Magnification.

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Units must be consistent before performing calculations. Most biological specimens are measured in micrometers (μm\mu m) or nanometers (nmnm).

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Unit conversion factors: 1 mm=103μm=106nm1 \text{ mm} = 10^3 \mu m = 10^6 nm. To convert from mmmm to μm\mu m, multiply by 10001000.

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Scale bars are often provided on micrographs. The magnification is calculated by measuring the length of the scale bar with a ruler and dividing it by the actual length indicated on the bar.

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When using a microscope, total magnification is calculated as: Magnification of eyepiece×Magnification of objective lens\text{Magnification of eyepiece} \times \text{Magnification of objective lens}.

📐Formulae

M=IAM = \frac{I}{A}

A=IMA = \frac{I}{M}

I=A×MI = A \times M

Total Magnification=Eyepiece Lens×Objective Lens\text{Total Magnification} = \text{Eyepiece Lens} \times \text{Objective Lens}

💡Examples

Problem 1:

An image of a plant cell measures 50 mm50 \text{ mm} in length. If the actual size of the cell is 100μm100 \mu m, calculate the magnification used.

Solution:

M=50 mm100μm=50,000μm100μm=×500M = \frac{50 \text{ mm}}{100 \mu m} = \frac{50,000 \mu m}{100 \mu m} = \times 500

Explanation:

First, convert the image size from mmmm to μm\mu m by multiplying by 10001000. Then, divide the image size (50,000μm50,000 \mu m) by the actual size (100μm100 \mu m) to find the magnification.

Problem 2:

A mitochondria is magnified ×20,000\times 20,000 and measures 40 mm40 \text{ mm} in a textbook diagram. What is the actual length of the mitochondria in μm\mu m?

Solution:

A=IM=40 mm20,000=0.002 mmA = \frac{I}{M} = \frac{40 \text{ mm}}{20,000} = 0.002 \text{ mm} Actual size in μm=0.002×1000=2μm\text{Actual size in } \mu m = 0.002 \times 1000 = 2 \mu m

Explanation:

Divide the image size by the magnification to get the actual size in mmmm. Finally, convert the result to micrometers by multiplying by 10001000.

Problem 3:

A scale bar on a micrograph represents 5μm5 \mu m. When measured with a ruler, the scale bar is 20 mm20 \text{ mm} long. Calculate the magnification of the micrograph.

Solution:

M=Measured length of scale barValue on scale bar=20,000μm5μm=×4,000M = \frac{\text{Measured length of scale bar}}{\text{Value on scale bar}} = \frac{20,000 \mu m}{5 \mu m} = \times 4,000

Explanation:

Convert the ruler measurement of the scale bar (20 mm20 \text{ mm}) into the same units as the scale bar value (5μm5 \mu m). Then divide the measured length by the real value.