Biology - Size of Specimens

A student measures a drawing of a bacterial cell to be $45 mm$ long. The actual length of the bacterium is $3 \mu m$. Calculate the magnification of the drawing.

First, convert the Image size ($I$) to micrometers: $45 mm \times 1000 = 45000 \mu m$ Next, apply the magnification formula: $M = \frac{I}{A}$ $M = \frac{45000 \mu m}{3 \mu m}$ $M = 15000 \times$

To calculate magnification, units must be consistent. Converting $45 mm$ to $45000 \mu m$ allows us to divide by the actual size of $3 \mu m$, resulting in a magnification of $15000$ times the original size.

A micrograph of a leaf cross-section has a magnification of $250 \times$. If the thickness of the leaf in the image is $3.5 cm$, what is the actual thickness of the leaf in micrometers ($\mu m$)?

First, convert the Image size ($I$) from $cm$ to $mm$: $3.5 cm = 35 mm$ Now, find the Actual size ($A$) in $mm$: $A = \frac{I}{M}$ $A = \frac{35 mm}{250} = 0.14 mm$ Finally, convert the actual size to micrometers: $0.14 mm \times 1000 = 140 \mu m$

The image size is measured as $3.5 cm$, which is $35 mm$. Dividing by the magnification ($250$) gives the actual size in $mm$ ($0.14 mm$). Multiplying by $1000$ converts this to the standard biological unit of micrometers.

A scale bar on an electron micrograph is $20 mm$ long and is labeled as representing $500 nm$. Calculate the magnification of the micrograph.

Convert the scale bar length ($I$) to $nm$: $20 mm \times 1000 = 20000 \mu m$ $20000 \mu m \times 1000 = 20,000,000 nm$ Apply the formula: $M = \frac{20,000,000 nm}{500 nm}$ $M = 40000 \times$

The scale bar acts as the 'Image' of the 'Actual' value it labels. By converting $20 mm$ into $20,000,000 nm$, we can divide by the labeled $500 nm$ to find that the image has been magnified $40,000$ times.