Looking into these two lenses, I'm getting the impression that for my Nikon D-90 with DX camera sensor that the f/1.8d would waste light that is cropped by the sensor whereas the f/1.4g would not as it is designed for the DX style. Further, the f/1.8d is not available as AF-S whereas the f/1.4g is AF-S.
Is my analysis correct and thus the f/1.4g will perform better with the DX style camera?
Answer
The Nikon AF-S 50mm f1.4 G is not designed for the smaller DX sensor and has the same image circle as the 1.8
Are you thinking of the AF-S 35mm f/1.8 G DX which is designed for a smaller sensor compared to the AF-S 35mm f/1.4G?
In any case the size of the image circle is of minor importance to the light gathering ability - only the aperture matters, as Evan states.
Despite a lens designed for a smaller image circle letting in less light total, it lets in the same light per unit area, so if you swap one lens for another designed for a larger image circle, but the same f-stop then your exposure would be the same.
The previous paragraph ignores vignetting, or the tendency for brightness to fall off across the frame. This usually gives lenses designed for a larger image circle a brightness advantage. There are other advantages to using lenses designed for the sensor you are using, such as sharpness, weight and better resistance to flare.
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