SME
Principles of Biology I · Problem type
Actual size from a micrograph
Use this for “A cell is 24 mm long in a photo taken at 4000×. How long is it really, and how wide is a field 8 cells across?”
Diagram
8 cells fill 48 μm end to end.
This is an example. Type your own values to start a new problem.
A (μm)
=
I (mm)
÷
M
I is the cell’s length in the photo and M the magnification, 4000 for 4000×; the picture draws the actual size.
Iₛ
Scale bar in the photo
example · mm
S
Length the scale bar stands for
calculated · μm
n
Cells across
example
F
Field width
calculated · μm
Formulas
A
=
I
M
×
1,000
6
=
24
4,000
×
1,000
S
=
Iₛ
M
×
1,000
10
=
40
4,000
×
1,000
F
=
n
×
A
48 = 8 × 6
Assumptions
•
Magnification is image size ÷ actual size, both in one unit: 1 mm = 1000 μm.
•
A scale bar is printed at the same magnification, so its length in the photo gives M too.
•
The cells lie end to end across the field and are all the same length.
Step-by-step
WE KNOW
I = 24 mm, M = 4,000×, Iₛ = 40 mm, n = 8
FIND
actual size (A), length the scale bar stands for (S), field width (F)
Step 1 · Find actual size (A)
Use A = I ÷ M × 1,000
Divide the image size by the magnification; × 1000 turns mm into μm.
A
=
24
4,000
×
1,000
A
=
0.006
×
1,000
A
=
6
μm
Step 2 · Find length the scale bar stands for (S)
Use S = Iₛ ÷ M × 1,000
The bar shrinks back by the magnification; × 1000 turns mm into μm.
S
=
40
4,000
×
1,000
S
=
0.01
×
1,000
S
=
10
μm
Step 3 · Find field width (F)
Use F = n × A
The cells end to end fill the field, so multiply one length by the count.
F
=
8
×
6
F
=
48
μm
Check
Put the numbers back in. Both sides should match.
6
=
24
4,000
×
1,000
✓
10
=
40
4,000
×
1,000
✓
48 = 8 × 6 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.