Calculating the image magnification on a video monitor can be accomplished first by determining the optical magnification and multiplying it by the electronic magnification.
Optical Magnification = Objective Mag. * Projection lens or “C-mount adapter Mag.
The objective magnification is expressed as 10x, 20x etc. and Projection lens or “C”-mount adapter is the optical path magnification that leads to the video camera.
Some typical magnification of the “C”-mount adapter are 0.35X, 0.5X, 0.65X, 0.75X, 1X.
Electronic Magnification = Monitor diagonal size / Camera chip diagonal size
The monitor’s diagonal size is usually expressed as 14”, 15”, 17”, 19”, 20”, 21”,...
The camera’s chip is expressed as 1/3”, 1/2”, 2/3” or 1”.
However, this is not the dimension we use. We need to use the diagonal dimension of the chip.
The table below represents the common chip sizes and their diagonal dimensions in millimetres and inches.

CHIP SIZE_____________DIAGONAL (mm)_____________DIAGONAL (INCHES)
1/3”___________________6____________________________0.24
½”____________________8____________________________0.31
2/3”__________________11____________________________0.43
1”____________________15,86_________________________0.63

The formula to calculate the final magnification of the image on the monitor is:
Objective Mag. * Projection lens or “C”-mount adapter Mag. * (Monitor diagonal size / Camera chip diagonal size).

Let’s make an example:

We have a microscope where a 2/3” camera with a 0.65 “C”-mount adapter is installed and the image is projected on a 21” monitor.
Actually we are using 20x objective
Microscope magnification: 20X (objective) * 10X (eyepiece) = 200X

Camera magnification: 20X (objective) * 0.65X (“C”-mount) * 21” (monitor) / 0.43” (chip size) =
20X * 0.65X * 48.83 = 634,79X

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