My idea of how a converter works is that it is an optical crop, for example a 1.4x converter turns your fx camera into a dx camera (roughly). The converter does this by magnifying the image so that a smaller part hits the sensor and more light is lost outside of the sensor. This has lead me to the thought that you get less light on the image when you use a converter compared to using a longer lense without converter.
Observe that I am not talking about the reduction of maximum aperture, which is due to the optical law of focal length / opening lense diameter = maximum aperture. And I am not talking about the small differences in transmission between lenses.
To make it clear I ask the question using an example: If I shoot an image using a 600/4 lense at 5.6 and then shoot the exact same image with equal settings using a 300/2.8 lense with a 2x converter, will the first image be lighter?
This may be basic stuff that I should know, but it has been puzzling me for so long that I must ask the question. If anyone has the equipment to examplify with photographs, it would be fantastic. But any thoughts are appreciated.