I have a theoretical question. Consider two lenses with same f-ratio but one has a larger focal length than the other (say 200 mm vs 50mm). Which lens would give better image quality when shooting portraits in low light considering the same composition, same lighting conditions and same f-ratio? Camera shake, hand-holding, motion blur is neglected.
"Image quality" commonly includes factors such as sharpness, resolution, distortions, aberrations, flaring, ghosting, etc. If all of these are identical between lenses, there would be no difference in image quality. In practice, it's unlikely you would have lenses that are exactly the same except for focal length.
There would also be no significant difference in low-light performance because you have posited that max aperture would be the same.
The F-stop system already accounts for light lost over distance. With the same F-number, lenses with longer focal lengths have physically larger apertures. (200/2 = 100) > (50/2 = 25).
There can be light transmission differences among lenses (T-stops). Focal length alone is insufficient to predict the T-stop of a lens.
There are two ways to achieve "same composition":
Move the 50mm lens closer to the subject. Some details will be relatively closer (noses) to the lens than others (ears). The closer details would be slightly easier to capture than the farther ones. However, it's not necessarily the case that the pores on people's noses are more important than those on their ears. Overall, such differences average out.
You may also consider the perspective change caused by viewing the subject from different distances to be a factor in "image quality".
Use both lenses from the same position and crop the image taken with the 50mm lens. This will result in a loss of resolution. Grain or noise may also appear to be increased. Many would consider these to be reduced "image quality". However, the variance between center and edge would be reduced. Some people consider that improved "image quality".
- Camera shake is more likely to affect a 200mm lens than a 50mm lens, even on tripod.
- With great distances (miles/kilometers), the atmosphere itself will affect image quality. For distances typical of portraits, the effect should be insignificant.
When imaging under feeble light conditions, need to use a large lens opening like f/2.8 or f/2 or f1.4 etc. Thus large f-number are a requisite, they capture more light. As alternatives, you can set the ISO high or use slow shutter speeds.
However, the key point that you are seeking: The f-number is a ratio that intertwines the focal length of the lens with its working iris diameter. Now a ratio is a dimensionless value. In other words, a lens set to f/4 affords the same exposure regardless. A 1000mm lens set to f/4 delivers the same exposure as a 25mm lens set to f/4. This is true for giant telescopic cameras as well. Thus there is no exposure advantage based on focal length differences.
However, portraiture is both an art and a science. As a general rule of thumb, facial distortion that results when working in too close is undesirable. A moderate telephoto fills this bill. Such a lash-up, 2X or 2.5X of normal focal length forces the photographer to step back and this deed greatly improves the resulting image of the human face. Let me aid, there are no rules in art, you are free to do your own thing.
The f-ratio defines the relation between the emitted light density on the scene and the arriving light density on the sensor.
The distance and focal length and crop factor and pixel size all are already compensated in that calculation.
That is important, for example, for placing off-camera flash. If you configure flash strength and distance for a certain ISO/f-ratio pairing, this ISO/f-ratio pairing on the flash will work with the same ISO/f-ratio settings on the camera regardless of where you move with the camera.
It also means you can hold a light meter before a spot of the subject that you want to meter in at nominal exposure, determine ISO/f-ratio for that spot of the subject, and then move with the camera to a different position and take the photograph with those settings.
If your camera has an exposure lock button, you can expose for a detail of the scene, then move to a different distance and take the shot.
The shorter FL lens is most likely to generate images with better technical IQ for two reasons.
The first is because the lower magnification reduces the impact of motion (camera shake, subject motion, handholding)... but you said you want to ignore that.
That leaves the second reason... in order to record the same subject composition the lens must be nearer the subject. This means the details are presented physically larger to the lens, which requires less lens resolution in order to see/transmit them, and less sensor resolution to record them.
I.e. if you want the greatest detail/resolution then get as close as possible (e.g. macro w/ a 50mm on extension tubes)...
But the 200mm and 50mm images would be very different in other aesthetic considerations, such as how much BG is included and how blurred it is.