Microscopy and Magnification: Principles, Calculations, and Cell Measurement

Historical Context of Microscopy

• Robert Hooke (1665):

  • Observed compartments in cork using his microscope.

  • He was the first to name these compartments "cells," which are the basic units of biology.

• Antonie van Leeuwenhoek:

  • Produced superior lenses a few years after Hooke, capable of magnifying up to $300 \times$.

  • He was the first to observe and describe single-celled organisms, specifically protozoa.

Types of Light Microscopy

• General Characteristics of Light Microscopes:

  • They are the most commonly used type of microscope.

  • Many are Compound Microscopes, meaning they use more than one lens to magnify the image.

  • Total Magnification is calculated as: $\text{Objective Lens} \times \text{Ocular Lens}$.

  • Oil Immersion: The use of oil increases the resolution of the image.

• Bright-field Microscope:

  • Utilizes a light source (lamp) and a series of lenses (condenser, objective, and eyepiece).

  • The image is viewed directly through the eyepiece.

• Dark-field Microscope:

  • Best suited for observing pale objects.

  • The specimen appears light against a dark background, which increases contrast and reveals more detail.

• Phase-contrast Microscope:

  • Used to examine living organisms or specimens that might be damaged or altered by slide attachment or staining.

  • Creates an image by altering the wavelengths of light rays as they pass through the specimen.

• Fluorescent Microscope:

  • Uses a direct Ultraviolet (UV) light source aimed at the specimen.

  • UV light increases both resolution and contrast.

  • Some cells fluoresce naturally, while others require staining.

  • Applied in immunofluorescence to detect specific pathogens and proteins.

Electron Microscopy (EM)

• Core Principles:

  • Uses electrons instead of light to visualize specimens.

  • The shorter wavelength of electrons provides significantly greater resolution than light.

  • Light microscopes cannot resolve structures closer than $200 \, nm$.

  • Electron microscopes have a magnification range of $10,000 \times$ to $100,000 \times$ (and higher).

  • Enables detailed views of bacteria, viruses, internal cellular structures, molecules, and large atoms.

  • Sample Preparation: Samples must be fixed (e.g., using parafilm) and coated with metal (e.g., gold), meaning the sample is dead.

• Transmission Electron Microscope (TEM):

  • Image Produced: 2D image of internal structures.

  • Electron Path: The electron beam passes through the specimen.

  • Magnification: $10,000 \times$ to $1,000,000 \times$.

  • Resolution: Approximately $0.2 \, nm$.

  • Preparation: Requires ultrathin sections of specimens, often stained with heavy metal salts.

• Scanning Electron Microscope (SEM):

  • Image Produced: 3D image of the specimen surface.

  • Electron Path: The electron beam scans the surface of the specimen.

  • Magnification: $1,000 \times$ to $10,000 \times$.

  • Resolution: Approximately $20 \, nm$.

  • Preparation: The specimen is coated with a thin layer of metal, such as gold.

Parts of the Compound Light Microscope

• Ocular Lens (Eyepiece): Remagnifies the image formed by the objective lens.

• Body: Transmits the image from the objective lens to the ocular lens using prisms.

• Arm: Supports the body and provides a handle for carrying.

• Objective Lenses: The primary lenses that magnify the specimen. Standard powers include:

  • Scanning (Low Power): $4 \times$

  • Low Power (Medium Power): $10 \times$

  • High and Dry (High Power): $40 \times$

  • Oil Immersion (High Power): $100 \times$

• Stage: Holds the microscope slide in position.

• Condenser: Focuses light through the specimen.

• Diaphragm: Controls the amount of light entering the condenser.

• Illuminator: The light source.

• Coarse Focusing Knob: Moves the stage up and down significantly to bring the image into focus.

• Fine Focusing Knob: Used for small, precise adjustments to sharpen the image.

• Base: The bottom support of the microscope.

General Principles of Microscopy

• Metric Units of Length (Calculations):

  • Metre (m): $1$

  • Decimetre (dm): $0.1 \, m$

  • Centimetre (cm): $0.01 \, m$

  • Millimetre (mm): $0.001 \, m$

  • Micrometre ($\mu m$): $0.000001 \, m$ (or $10^{-6} \, m$)

  • Nanometre (nm): $0.000000001 \, m$ (or $10^{-9} \, m$)

  • Picometre (pm): $0.00000000001 \, m$ (or $10^{-12} \, m$)

• Contrast:

  • The difference in intensity between two objects or between an object and its background.

  • Essential for determining resolution.

  • Can be increased through staining or using light that is in phase.

• Magnification:

  • The number of times an image is larger than the real size of the object.

  • Calculated based on the power of the objective and eyepiece lenses.

• Resolution:

  • The ability to distinguish between two separate points.

  • Determined by the wavelength of radiation used.

  • Higher resolution allows for greater detail visibility.

Calculation Types and Formulas

The Magnification Formula

$M = \frac{I}{A}$ Where:

• $M$ = Magnification

• $I$ = Image size (measured with a ruler)

• $A$ = Actual size of the object

Example 1: Calculating Magnification

• Given: Image size = $30 \, mm$; Specimen size = $3 \, \mu m$.

1. Convert quantities to the same unit: $30 \, mm \times 1000 = 30,000 \, \mu m$.

2. Apply formula: $M = \frac{30,000 \, \mu m}{3 \, \mu m}$.

3. Result: Magnification is $10,000 \times$.

Example 2: Calculating Actual Size of an Organelle

• Given: A mitochondrion is magnified $100,000 \times$. The image size (measured by ruler) is $50 \, mm$.

1. Rearrange formula: $A = \frac{I}{M}$.

2. Apply formula: $A = \frac{50 \, mm}{100,000}$.

3. $A = 0.0005 \, mm$.

4. Convert to micrometres: $0.0005 \, mm \times 1000 = 0.5 \, \mu m$.

5. Result: Actual size is $0.5 \, \mu m$.

Example 3: Scale Bar Calculation for a Chloroplast

• Given: Image size measured as $50 \, mm$. Magnification calculated from a scale bar (where $2 \, \mu m$ measures $30 \, mm$ on paper).

1. Calculate magnification from scale bar: $M = \frac{30 \, mm}{2 \, \mu m} = \frac{30,000 \, \mu m}{2 \, \mu m} = 15,000 \times$.

2. Calculate actual size of organelle: $A = \frac{I}{M} = \frac{50 \, mm}{15,000} = \frac{50,000 \, \mu m}{15,000}$.

3. Result: Actual size is $3.3 \, \mu m$.

Measuring Cells using Microscopic Scales

• Measurement Tools:

  • Eyepiece Graticule: A transparent scale (usually 100 divisions) placed in the microscope eyepiece. It has no absolute units until calibrated.

  • Stage Micrometer: A microscope slide with a finely divided scale marked on its surface (providing accurate, known reference dimensions).

• Field of View Estimation:

  • If the diameter of the field of view is known (e.g., $1 \, mm$ via a stage micrometer), cell size can be estimated.

  • Example: Field of view = 30 divisions ("pitch"); 1 division = $10 \, \mu m$.

  • Two onion cells span 30 divisions: $30 \times 10 \, \mu m = 300 \, \mu m$ total length.

  • One onion cell = $300 \, \mu m \div 2 = 150 \, \mu m$.

• Calibration of Eyepiece Graticule:

  1. Align the stage micrometer scale with the eyepiece graticule scale.

  2. Identify points where the lines of both scales line up perfectly.

  3. Scenario: $.0$ (micrometer) aligns with $1.0$ (graticule). At another point, the $68$ mark (micrometer) aligns with the $9.0$ mark (graticule).

  4. The distance between these points accounts for $80$ small eyepiece graticule markings.

  5. This distance on the stage micrometer is $18$ markings.

  6. Each marking on the stage micrometer = $0.01 \, mm$.

  7. $18 \times 0.01 \, mm = 0.18 \, mm = 180 \, \mu m$.

  8. Therefore, $1$ small eyepiece marking = $180 \, \mu m \div 80 = 2.25 \, \mu m$.

• Calculating Actual Width after Calibration:

  • Given: A plant cell measures $23$ eyepiece graticule units long.

  • Calculation: $23 \text{ units} \times 2.25 \, \mu m/\text{unit} = 51.75 \, \mu m$.

  • Result: Actual width of the plant cell is $51.75 \, \mu m$.