Understand the relationship
The reasoning behind the result
Visual magnification combines the objective and eyepiece
Mvisual = Mobjective Mintermediate Meyepiece
The objective forms an enlarged intermediate image. The eyepiece then acts as a magnifier for observation. In the conventional stated visual magnification, their factors multiply, together with any known intermediate magnifier. All factors here are positive magnitudes; image inversion and orientation are not represented.
The effective objective factor belongs to the actual system. In an infinity-corrected microscope it depends on the objective and tube-lens focal lengths. A marked objective value cannot be assumed unchanged after modifying that configuration. Enter the established effective factor rather than counting a tube-lens adjustment twice.
A camera path has a different endpoint
Mcamera = Mobjective Mrelay
Camera mode reports lateral image magnification at the sensor: an ideal specimen length multiplied by this factor gives its image length at the sensor. The relay factor represents the camera-path optics after the effective objective. An eyepiece factor is not included unless its actual contribution is already part of a separately established relay factor.
Monitor size, browser zoom, printed size, digital resizing and sensor pixel pitch are absent from this optical product. They cannot be inferred from an objective name or camera adapter factor. The pixel calibration tool handles a known sensor pitch and image scaling as a separate measurement task.
A target solve exposes the missing factor
Mobjective,target = Mvisual,target / (Mintermediate Meyepiece)
Dividing the target product by the two known factors gives the required effective objective factor. This is a continuous arithmetic result, not a selection from commercially available objectives. Multiple targets can be evaluated without losing their names or intermediate assumptions.
The comparison chart shows the final factor of every setup under the single chosen convention. The ledger preserves the factors that produced it, so identical totals do not hide different optical paths. Visual and sensor-lateral results are never mixed in one comparison.
Larger images do not establish finer resolution
Increasing magnification can spread an existing image over more apparent angle or sensor area without revealing additional specimen information. Numerical aperture, wavelength, contrast, aberrations, sampling and calibration are separate quantities.
The result therefore carries no useful-power grade, resolution limit, equipment compatibility claim or specimen-size estimate. In particular, multiplying an eyepiece power does not supply an eyepiece field number.
Follow the numbers
Trace a 500× visual setup and a 20× camera setup
- A 40× effective objective with a 1.25× intermediate magnifier forms an intermediate factor of 40 × 1.25 = 50.
- With a 10× eyepiece, the visual product is 50 × 10 = 500×.
- A separate camera path using the same 40× effective objective and a 0.5× relay has a sensor-lateral magnification of 40 × 0.5 = 20×. The eyepiece is not part of that path.
- For a visual target of 300× with a 1.5× intermediate factor and 10× eyepiece, the required objective factor is 300 / (1.5 × 10) = 20×.
The arithmetic follows the declared optical path; it does not equate visual apparent size with sensor image size or resolved detail.
Quick guide
How to use this calculator
- Choose the actual viewing path. Visual and camera magnifications describe different image relationships.
- Add a row for each setup using effective factors established for that configuration. A factor of one means no change at that stage.
- For a target visual magnification, enter the chosen target, intermediate factor and eyepiece factor; read the required effective objective factor.
- Review every stage in the comparison ledger. Check calibration and resolved detail separately before using an image for measurement.
Calculation method
Calculation and interpretation
Follow each known optical factor through to the magnification it actually describes.
Mvisual = Mobjective · Mintermediate · Meyepiece; Mcamera = Mobjective · Mrelay; Mobjective,target = Mvisual,target / (Mintermediate · Meyepiece).
Worked example
Trace a 500× visual setup and a 20× camera setup
The arithmetic follows the declared optical path; it does not equate visual apparent size with sensor image size or resolved detail.
Mvisual = Mobjective · Mintermediate · Meyepiece; Mcamera = Mobjective · Mrelay; Mobjective,target = Mvisual,target / (Mintermediate · Meyepiece).
Supported inputs
Precision and limits
Established factors for one optical path
Use independently known effective factors for the actual tube lens, objective, intermediate optics and relay. This tool does not model optical compatibility, aberration correction, focus travel, vignetting or image orientation.
Numerical calculation, not calibration
Positive dimension, scale and magnification inputs support 10⁻¹² through 10¹² in their selected units. Signed displacement components may be exactly zero; nonzero components must have an absolute magnitude from 10⁻¹² through 10¹². These are numerical bounds, not equipment specifications or accuracy claims. Nominal factors do not replace a stage-micrometer calibration of the final image.
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