Sensor size ↔ image circle diameter
The lens has to be able to illuminate the complete sensor area in order to avoid shading and vignetting.
Pixel size ↔ optical resolution
The lens has to be able to resolve the pixel size. The better the optical resolution of a lens, the better detailed structures can be reproduced. The optical quality of a lens is defined by the MTF (modulation transfer function) relating to resolution along with the optical distortion.
Object resolution ↔ magnification
In order to resolve the details of an object and to ensure definite edge detection, the detail should be reproduced across about 4 pixels. Thus the required magnification is dependent on the required object resolution and the respective pixel size. Only the knowledge of all these application specific parameters permits the correct selection of the optimum lens to meet the required field of view and image quality.
Camera sizes are often quoted in imperial units, although this does not precisely infer the physical dimensions of the sensor. It is actually a legacy from the pre-digital era, when many cameras used vacuum tubes.
When selecting a lens it is very important to ensure that the format size matches or exceeds that of the chosen sensor. The maximum sensor size is always part of the description of a lens. Sometimes the maximum image circle diameter is also indicated. This is a circle with the sensor diagonal as diameter.