1. Microscope Calculations
Math + Science = FUN

2. How to Calculate Total Magnification
To calculate the total magnification
of a compound microscope, you
must multiply the magnification of
the ocular lens (lens in the
eyepiece) by the magnification of
the objective lens.
Total Magnification Formula
Total Mag = Mag(ocular lens) x Mag(objective lens)

3. Total Magnification
What would the magnification of a microscope with the ocular lens that enlarges the image by 10x and an objective lens that enlarges the image by 10x(medium power)?
Total Mag = Mag(ocular lens) x Mag(objective lens)
=10 x 10
=100x
Therefore the magnification with an ocular lens of 10x and an objective lens of 10x is 100x.

4. Total Magnification
What about for microscopes with an ocular lens of 10x and objective lenses of:
4x (low power)
40x (high power)
What lenses would you combine if you wanted to magnify an object:
100x
400x

5. Measuring the Field of View
Field of View (FOV) – The diameter of the circle of light that you see when looking into a microscope.
As the power gets greater, the field of view gets smaller.
Try measuring the FOV on low power
by using your agenda ruler.
The field of view on low power is
4mm.

6. Calculating FOV for Medium & High Power
It is very difficult to measure the FOV under medium and high power lenses since the magnification is so high. However, you can use formulas to calculate them.
Field of View Formulas
𝑀𝑒𝑑 𝑭𝑶𝑽=𝐿𝑜𝑤 𝐹𝑂𝑉 𝑥 𝐿𝑜𝑤 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑀𝑒𝑑 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
𝐻𝑖𝑔ℎ 𝑭𝑶𝑽=𝐿𝑜𝑤 𝐹𝑂𝑉 𝑥 𝐿𝑜𝑤 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝐻𝑖𝑔ℎ 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
Try calculating the medium and high FOV when the low FOV is 4mm.

7. Calculating FOV for Medium & High Power
𝑀𝑒𝑑 𝑭𝑶𝑽=𝐿𝑜𝑤 𝐹𝑂𝑉 𝑥 𝐿𝑜𝑤 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑀𝑒𝑑 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
=4𝑚𝑚 𝑥 4𝑥 10𝑥
=4𝑚𝑚 𝑥 0.4
= 1.6 mm or 1600µm
𝐻𝑖𝑔ℎ 𝑭𝑶𝑽=𝐿𝑜𝑤 𝐹𝑂𝑉 𝑥 𝐿𝑜𝑤 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝐻𝑖𝑔ℎ 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
=4𝑚𝑚 𝑥 4𝑥 40𝑥
=4𝑚𝑚 𝑥 0.1
= 0.4 mm or 400µm

8. Estimating size of microscope objects
Using what you know about FOV calculations, you can now estimate the size of your specimen.
Estimating Size Formula
𝑬𝒔𝒕𝒊𝒎𝒂𝒕𝒆𝒅 𝑆𝑖𝑧𝑒= 𝐹𝑂𝑉 # 𝑜𝑓 𝑆𝑝𝑒𝑐𝑖𝑚𝑒𝑛𝑠
FOV can represent low, medium, or high power. Number of specimens represents the number that can fit across the FOV diameter.
What if 4 of your specimens could fit into the field of view? What would be the estimated size of the original specimen?

9. Formula Review Total Magnification
Total Mag = Mag(ocular lens) x Mag(objective lens)
Field of View Diameter (Length)
Low FOV – Can be measured using a ruler
under the low-power lens.
𝑀𝑒𝑑 𝑭𝑶𝑽=𝐿𝑜𝑤 𝐹𝑂𝑉 𝑥 𝐿𝑜𝑤 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑀𝑒𝑑 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
𝐻𝑖𝑔ℎ 𝑭𝑶𝑽=𝐿𝑜𝑤 𝐹𝑂𝑉 𝑥 𝐿𝑜𝑤 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝐻𝑖𝑔ℎ 𝑃𝑜𝑤𝑒𝑟 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
Estimated Size of Specimen
𝑬𝒔𝒕𝒊𝒎𝒂𝒕𝒆𝒅 𝑆𝑖𝑧𝑒= 𝐹𝑂𝑉 # 𝑜𝑓 𝑆𝑝𝑒𝑐𝑖𝑚𝑒𝑛𝑠