The connection between your microscope and camera.
There are literally hundreds of potential combinations with many different camera and microscope types. The most fundamental information you will need when deciding which c-mount adapter you need are as follows:
What make and model is your microscope?
This information is important as there will be different focal positions (point at which image data will be collected on the cameras chip) for different manufacturers microscopes. Modern microscopes will tend to have the model type on the microscope body, sometimes near the serial number. As an alternative the microscope manufacturer should be able to identify the microscope by its description or by a photograph.
What make and model is the camera you are trying to attach?
This is an important piece of information as it usually determines the type of thread or fitting the c-mount adapter should have.
What port will you be using?
It is not always possible to connect a camera via a dedicated camera port (sometimes referred to as trinocular tube or beamsplitter). It is important that you identify which port will be used to accept the c-mount.
Is a magnification necessary?
The camera chip (CCD) will be of a certain dimension and will require the appropriate magnification within the c-mount adapter which is sometimes referred to as a relay lens. A good rule of thumb is that whichever size the CCD is as a decimal is what it requires in magnification to fill the viewfield. For example a 2/3” CCD (0.67”) requires a 0.7x c-mount. The CCD size should always be made available by the manufacturer.
It is always remembering that a lower magnification will give a wider field of view and generally brighter images for shorter exposures.