Magnification and Resolution

This lesson covers:

  1. The definitions of magnification and resolution
  2. How to calculate magnification
  3. How to calibrate a microscope 

Magnification

Magnification is how many times larger an image is than the object. 


For example, here the image is 1,000 larger than the object, so its magnification is x 1,000.

Diagram showing an image magnified 1,000 times larger than the object.

Resolution

Resolution is the ability to distinguish between two separate points (or how detailed the image is). 


For example, both images here have the same magnification, but the left image has a higher resolution.

Comparison of two microscope images showing the difference between high and low resolution.

Calculating magnification

To calculate magnification, you need to know the image size and the object size:

  • Image size - How large the object appears when you view it through a microscope.
  • Object size (actual size) - The real size of the object.


The equation for calculating magnification is:

magnification =image sizeobject size\text{magnification }=\frac{\text{image size}}{\text{object size}}

When calculating magnification, all lengths must be in the same unit. This may require converting from one unit to another.

Diagram showing unit conversions from centimetres to millimetres to micrometres to nanometres.

Calibrating a microscope 

When viewing a specimen, you can measure its length or width using an eyepiece graticule. This is a small scale (usually from 1 to 100) placed within the eyepiece.

Diagram showing the calibration of a microscope using an eyepiece graticule and a stage micrometer.

However, the scale divisions of the eyepiece graticule will represent different real-world distances, depending on the magnification of the objective lens you are looking through. This means the graticule needs to be calibrated for each objective lens.


A stage micrometer is used to calibrate the eyepiece graticule. This is a glass slide with a scale measured in µm. 


The graticule is calibrated as follows: 

  1. Fix the stage micrometer into place on the stage.
  2. Look through the eyepiece to line up the micrometer and the graticule. 
  3. Count the number of graticule divisions that fit into one micrometer division.
  4. Use the formula below to calculate the size of each graticule division at that magnification:


graticule division =size of one micrometer divisionnumber of graticule divisions\text{graticule division }=\frac{\text{size of one micrometer division}}{\text{number of graticule divisions}}

Worked example - Calibrating a light microscope 

View through a light microscope eyepiece showing a stage micrometer aligned with a graticule scale.

The image above represents what you'd see if you looked into the eyepiece of a light microscope. It shows a stage micrometer lined up with a graticule scale.


Each division on the micrometer represents 10 µm. Calculate the size of each graticule division.

Step 1: Count the number of graticule divisions in one micrometer division

40 graticule divisions = 1 micrometer division


Step 2: Equation

graticule division =size of one micrometer divisionnumber of graticule divisions\text{graticule division }=\frac{\text{size of one micrometer division}}{\text{number of graticule divisions}}


Step 3: Substitution and correct evaluation

graticule division =1040\text{graticule division }=\frac{10}{40}

graticule division =0.25\text{graticule division }=0.25 µm

Worked example - Calculating magnification

A plant cell in a micrograph measures 40 mm in width. If the real width of the plant cell is actually 20 µm, what is the magnification?


Step 1: Equation

magnification =object sizeimage size​


Step 2: Conversion

to convert from mm into μm, multiply by 1,000

image size =40×1,000=40,000 μm

object size =20 μm 


Note: the units for image size and object size need to be the same before they are put into the magnification calculation


Step 3: Substitution and correct evaluation

magnification =2040,000​

magnification = x20,000

Worked example - Calculating image size

A sperm cell is 5 µm long. How long will it appear in mm when viewed under a microscope with a magnifying power of x 1,500?


Step 1: Equation

magnification =object sizeimage size​


Step 2: Rearrangement

image size = magnification× object size


Note: we need to rearrange the equation to make image size the subject


Step 3: Substitution and correct evaluation

image size =1,500×5

image size =7,500 µm


Step 4: Conversion

to convert µm into mm, divide by 1,000

image size =1,0007,500​

image size =7.5 mm