Lens opening, amount of light through new pancake versus older lenses
You're right... sort of? I'll preface this by saying I know nothing of lens design, but here's what I've heard from others:
The 30mm f2 is probably a modified double gauss or very conventional lens design. So the front element needs to be 15mm (30/2) at largest.
The zoom is likely a retrofocus (inverse telephoto) lens, which telephoto group behind the main optical assembly (or something) to move the optical center forward. Normally a 30mm lens focuses at infinity 30mm from the sensor... and that puts the rear element very close to the sensor. Retrofocus lenses can shift the front element a lot further forward, making room for a mirror box.
This is why Leica lenses (some of which are now retrofocus for performance reasons) are smaller than their SLR equivalents. And remember ultra-wides for SLRs have long had way bigger front elements for their slow speeds than fast fifties.
One side effect of this is that the extra glass in the zoom makes its effective transmission a bit lower, in theory, so the 30mm f2 might have a higher t-stop, or the opposite of what you'd expect. But the retrofocus lenses have less fall off, which is a product of distance between the rear element and lens (I think?). So to that extent they do allow more light in. There should be less fall off. In theory.
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