Microscope Magnification Calculator

Total microscope magnification is the product of objective magnification and eyepiece magnification. Standard combinations range from 40x to 1000x for biological samples.

🔬 Optics📐 M = Mₒₕⱼ × Mᵉᵙᵉ🧪 Biology

Objective Magnification

Eyepiece Magnification

Numerical Aperture (NA)

Wavelength (nm)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Total Magnification	M	M = M_obj × M_eye	×
Objective Mag	M_obj	4x, 10x, 40x, 100x	×
Eyepiece Mag	M_eye	Usually 10x or 15x	×
Resolution	d	d = 1.22λ/(2 NA)	nm

Step-by-Step Examples

Example 1

Standard Setup

Objective 40x, eyepiece 10x.

M = 40 * 10 = 400x
Resolution: NA=0.65, lambda=550 nm: 0.52 um

✓ 400x magnification, 0.52 um resolution

Example 2

Oil Immersion

Objective 100x oil (NA=1.3), eyepiece 10x.

M = 100 * 10 = 1000x
Resolution = 1.22*550/(2*1.3) = 258 nm

✓ 1000x, 258 nm resolution — limit of optical microscopy

Example 3

Low Power Survey

4x objective, 10x eyepiece.

M = 4 * 10 = 40x
Useful for initial scan of large samples

✓ 40x — low power survey magnification

Real-World Applications

🧬

Biology

Cell structures visible at 400x; bacteria at 1000x with oil immersion.

💉

Medical Diagnosis

Pathology uses 100-400x to examine tissue sections for disease.

🧪

Microbiology

Bacteria (1-10 um) visible at 400-1000x. Viruses require electron microscopy.

💎

Materials Science

Metallographic microscopes examine grain structure in metals at 50-1000x.

Common Mistakes to Avoid

⚠️

Total magnification is product, not sum

M = M_obj * M_eye. 40x objective with 10x eyepiece = 400x total, not 50x.

⚠️

Higher magnification needs oil immersion

Above 600x, oil immersion (n=1.515) between objective and slide increases NA and resolution.

⚠️

Empty magnification

Beyond ~1000x in optical microscopy, magnification is empty — no additional detail is revealed due to diffraction limit.

Frequently Asked Questions

What is empty magnification? ▾

Magnification beyond what resolution supports. You see larger but not more detail. Optical microscopes are limited to ~1000x useful magnification.

What does NA mean? ▾

Numerical Aperture = n*sin(alpha) where alpha is half the acceptance angle. Higher NA captures more diffracted light, giving better resolution.

Why use oil immersion? ▾

Oil (n=1.515) between objective and coverslip increases NA from ~0.65 (air, 40x) to ~1.3 (oil, 100x), improving resolution by 2x.

How small can optical microscopes see? ▾

Diffraction limit: d = lambda/(2*NA) ~ 200 nm with green light and NA=1.4. Viruses (20-200 nm) cannot be resolved. Electron microscopes needed.

What is confocal microscopy? ▾

Uses pinhole to reject out-of-focus light, allowing 3D imaging by optical sectioning. Same magnification as conventional but much better contrast.

Related Physics Calculators

Formula Explorer connections

Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.

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