The Compound Microscope
Simple Explanation
A compound microscope uses two converging lenses — an objective lens (close to the tiny object) and an eyepiece lens (close to the eye) — to magnify a small object far more than a single lens could alone.
Why Do We Need It?
Combining two lenses in sequence, each magnifying the image the previous one produced, is the key trick behind every high-magnification optical instrument — the same principle scales up to research-grade microscopes.
See It
Two vertical lines representing the objective lens on the left and the eyepiece lens on the right, separated by the tube length, both centered on the same optical axis
Formula
Compound Microscope Magnifying Power
M ≈ (L/f₀)(D/fₑ)
A compound microscope's total magnification comes from two lenses working together: the objective lens creates a magnified real image, which the eyepiece lens then magnifies again as a virtual image.
- M
- — total magnifying power (dimensionless)
- L
- — tube length — the distance between the objective and eyepiece lenses, in metres (m)
- f₀
- — focal length of the objective lens, in metres (m)
- D
- — the near point distance of the eye, conventionally 0.25 m
- fₑ
- — focal length of the eyepiece lens, in metres (m)
When to use it: Whenever a compound microscope's total magnifying power needs to be estimated from its lens focal lengths and tube length.
Worked Example
Find a compound microscope's magnifying power
A microscope has a tube length of 0.18 m, an objective lens of focal length 0.005 m, and an eyepiece of focal length 0.025 m. Find its magnifying power (using D=0.25 m).
Why Does This Work?
The objective lens forms an enlarged real image of the tiny object; the eyepiece lens then acts like a simple magnifying glass on THAT already-enlarged image — magnifying it further — so the two magnification factors multiply together rather than simply adding.
Real-Life Example
Examining a blood sample under a lab microscope
A lab technician examines blood cells (only a few micrometres across) using a compound microscope with interchangeable objective lenses.
Switching to an objective lens with a shorter focal length increases L/f₀, boosting the total magnification — exactly why microscopes offer multiple objective lenses for different levels of detail.
Practice
A microscope has L=0.16 m, f₀=0.004 m, and fₑ=0.02 m. Find its magnifying power (D=0.25 m).
HardCommon mistake
Adding the two magnification factors instead of multiplying them — each lens magnifies the image the previous lens already produced, so their effects COMPOUND (multiply), not simply add.
Quick Review
- M ≈ (L/f₀)(D/fₑ).
- Objective forms a magnified real image; eyepiece magnifies it again.
- The two magnification factors multiply, not add.