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Organization of the Organism - Size of specimens (Magnification)

Grade 11A LevelBiology

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

🔑Concepts

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Magnification is defined as how many times larger an image is compared to the actual size of the object being viewed.

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The standard formula used in Biology is represented by the triangle I=A×MI = A \times M, where II is the Image size, AA is the Actual size, and MM is the Magnification.

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Units must be consistent before performing calculations. If the image size is in mmmm and the actual size is in μm\mu m, one must be converted to match the other.

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Conversion factors: 1 mm=1000 μm1\text{ mm} = 1000\text{ }\mu\text{m} and 1 μm=1000 nm1\text{ }\mu\text{m} = 1000\text{ nm}.

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When using a scale bar, the magnification is calculated by measuring the length of the scale bar with a ruler (II) and dividing it by the value written on the scale bar (AA).

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Calculated magnification should usually be rounded to the nearest whole number or expressed in scientific notation if it is very large (e.g., in electron microscopy).

📐Formulae

Magnification(M)=Size of Image (I)Actual Size of Specimen (A)Magnification (M) = \frac{\text{Size of Image (I)}}{\text{Actual Size of Specimen (A)}}

Actual Size (A)=Size of Image (I)Magnification (M)Actual\ Size\ (A) = \frac{\text{Size of Image (I)}}{\text{Magnification (M)}}

Image Size (I)=Actual Size (A)×Magnification (M)Image\ Size\ (I) = Actual\ Size\ (A) \times Magnification\ (M)

1 mm=103 μm1\text{ mm} = 10^3\text{ }\mu\text{m}

1 μm=103 nm1\text{ }\mu\text{m} = 10^3\text{ nm}

💡Examples

Problem 1:

A photomicrograph of a plant cell shows a nucleus with an image diameter of 12 mm12\text{ mm}. If the actual diameter of the nucleus is 6 μm6\text{ }\mu\text{m}, calculate the magnification.

Solution:

M=12,000 μm6 μm=×2000M = \frac{12,000\text{ }\mu\text{m}}{6\text{ }\mu\text{m}} = \times 2000

Explanation:

First, convert the image size from mmmm to μm\mu m to match the units of the actual size: 12 mm×1000=12,000 μm12\text{ mm} \times 1000 = 12,000\text{ }\mu\text{m}. Then, use the formula M=IAM = \frac{I}{A}.

Problem 2:

An image of a red blood cell is magnified ×5000\times 5000. The length of the cell in the image is 35 mm35\text{ mm}. Calculate the actual length of the cell in μm\mu m.

Solution:

A=35 mm5000=0.007 mmA = \frac{35\text{ mm}}{5000} = 0.007\text{ mm} 0.007 mm×1000=7 μm0.007\text{ mm} \times 1000 = 7\text{ }\mu\text{m}

Explanation:

Use the formula A=IMA = \frac{I}{M}. Divide the image size (35 mm35\text{ mm}) by the magnification (50005000) to get the actual size in mmmm. Finally, convert mmmm to μm\mu m by multiplying by 10001000.

Problem 3:

A scale bar on an electron micrograph is 2 cm2\text{ cm} long and is labeled 100 nm100\text{ nm}. Calculate the magnification of the image.

Solution:

I=2 cm=20 mm=20,000 μm=20,000,000 nmI = 2\text{ cm} = 20\text{ mm} = 20,000\text{ }\mu\text{m} = 20,000,000\text{ nm} M=20,000,000 nm100 nm=×200,000M = \frac{20,000,000\text{ nm}}{100\text{ nm}} = \times 200,000

Explanation:

To calculate magnification from a scale bar, measure the bar's length (I=2 cmI = 2\text{ cm}). Convert this measurement to the same units as the scale bar label (100 nm100\text{ nm}). Since 2 cm=20,000,000 nm2\text{ cm} = 20,000,000\text{ nm}, the magnification is 20,000,00020,000,000 divided by 100100.