Microscope and Drawing Magnification Principles and Calculations

Definition and Fundamentals of Magnification

• Magnification is defined as the number of items an object is enlarged or reduced by a lens system of a microscope or by a drawing.
• Materials Required for Magnification Determination:
  • Compound microscope
  • Celluloid ruler
  • Sea shell
  • Sea star
  • Frog's blood smear

Microscope Magnification

• Lens System Mechanism:

  • In microscopes, magnification is achieved by a system of curved lenses situated in the ocular (eyepiece) and objective.
  • The objective magnifies the specimen to a definite size.
  • The ocular further magnifies the image formed by the objective.
  • The resulting image seen by the eye has a magnification equal to the product of the magnification of the two lens systems.

• Linear Magnification ($LM$):

  • The total magnification in either a compound or a binocular microscope is known as Linear Magnification.
  • Formula for Linear Magnification:     $LM = OcM \times ObM$     Where:
  • $LM$ = Linear magnification
  • $OcM$ = Magnification of ocular used
  • $ObM$ = Magnification of objective used

• Reading Magnification Markings:

  • Ocular Lens: Stamped $5\times$ magnifies five times ($5\times$); stamped $10\times$ magnifies ten times ($10\times$).
  • Low Power Objective: Stamped $10\times$ (or another numerical figure) represents the objective magnification.

• Theoretical Magnification Calculations:

  • Calculation Example 1 (Low Power Objective):
  • Specimen size = $1\,mm$
  • Objective lens = $10\times$ (magnifies specimen theoretically to $10\,mm$)
  • Ocular lens = $10\times$
  • Total Linear Magnification calculation:       $LM = 10\times \times 10\times = 100\times$
  • Calculation Example 2 (High Power Objective):
  • High power objective = $40\times$
  • Ocular lens = $15\times$
  • Total Linear Magnification calculation:       $LM = 15\times \times 40\times = 600\times$

• Microscope Magnification Task:

  • Compute the linear magnification of a microscope under:
  1. Low power objective
  2. High power objective
  • Complete mathematical solutions must be provided for both computations.

Magnification of a Drawing

• Definition and Purpose:

  • Whenever a biological drawing is made, an indication of its size relative to the actual object must be provided.
  • The magnification value indicates how much larger or smaller the drawing is than the actual specimen size.

• Formula for Magnification of a Drawing ($M$):   $M = \frac{SD}{SO}$   Where:

  • $M$ = Magnification of the drawing
  • $SD$ = Size of the drawing
  • $SO$ = Actual size of the object

• Practical Calculation Example:

  • Actual specimen length ($SO$) = $10\,mm$
  • Drawing length ($SD$) = $100\,mm$
  • Resulting magnification calculation:     $M = \frac{100\,mm}{10\,mm} = 10$
  • Scientific Notation Format: Written as $\times 10$ or $10\times$ directly beneath the drawing.

• Essential Rules for Measurement:

  • Corresponding parts must be measured in both the drawing and the actual object.
  • Measurements for both drawing size ($SD$) and actual object size ($SO$) must always be expressed in the exact same unit of measurement.

Determination of Actual Size of Microscopic Objects

• Calibration Calibration Constant ($C$):

  • Determination of a microscopic object's actual size requires specialized devices: an eyepiece micrometer and a stage micrometer.
  • These devices are used to establish the calibration constant of the microscope.
  • Formula for Calibration Constant ($C$):     $C = \frac{SMD}{sd}$     Where:
  • $C$ = Calibration constant
  • $SMD$ = Value of included stage micrometer divisions (where the unit of measurement of each division is known)
  • $sd$ = Number of included eyepiece micrometer space divisions

• Step-by-Step Procedure to Find Actual Size ($SO$):

  1. Insert the eyepiece micrometer into the ocular lens of the microscope.
  2. Count the number of micrometer space divisions ($sd$) covered by the image of the specimen under the Low Power Objective (LPO).
  3. Repeat the division count ($sd$) under the High Power Objective (HPO).
  4. Compute the actual size of the specimen by multiplying the calibration constant (in millimeters) by the number of included eyepiece micrometer space divisions.

• Formula for Actual Specimen Size ($SO$):   $SO = C \times sd$   Where:

  • $SO$ = Actual size of specimen in millimeters ($mm$)
  • $C$ = Calibration constant (in millimeters)
  • $sd$ = Number of included space divisions

Laboratory Exercises and Computational Steps

• Sea Shell Drawing Magnification:

  1. Obtain a sea shell specimen.
  2. Draw a $5\,cm$ long illustration of the sea shell on paper.
  3. Calculate the magnification of the drawing using $M = \frac{SD}{SO}$.

• Sea Star Drawing Magnification:

  1. Obtain a sea star specimen.
  2. Draw a corresponding $5\,cm$ diameter illustration of the sea star.
  3. Calculate the magnification of the drawing.

• Frog's Blood Smear Microscopic Analysis:

  1. Focus a prepared slide of frog's blood smear under the Low Power Objective (LPO).
  2. Select a single red blood cell.
  3. Using an eyepiece micrometer, count the number of spaces spanned by the selected red blood cell under LPO.
  4. Repeat the space count for the same cell under the High Power Objective (HPO).

• Actual Size and Averaging Procedures:

  1. Compute the actual size ($SO$) of the red blood cell under LPO using the formula $SO = C \times sd$.
  2. Compute the actual size ($SO$) of the red blood cell under HPO using the formula $SO = C \times sd$.
  3. Calculate the average actual size of the red blood cell from the LPO and HPO actual sizes.

• Red Blood Cell Drawing and Final Magnification Calculations:

  1. Create a drawing of the red blood cell with a diameter of $5\,cm$.
  2. Calculate the magnification of the drawing using the eyepiece micrometer space counts and calibration constants for both LPO and HPO.
  3. Solve for the final drawing magnification using the calculated average actual size.

• Presentation and Derivation Principles:

  • Full computations must be shown for all steps.
  • Indicate the calculated magnification value (e.g., $10\times$ or $\times 10$) directly beneath each drawing.
  • Mathematical Derivation Note: When a drawing is accompanied by its magnification, an estimate of the actual size of the object can be mathematically derived using the rearranged formula:     $SO = \frac{SD}{M}$