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Entrance pupil size and front element diameter are extremely well correlated for longer focal lengths, but as you get into ultrawides the correspondence stops. Our 8mm f/4.0 lens should have a tiny front element. The answer is that for a lens to be f/4.0 the physical hole in the lens that appears to be 2mm wide, must be visible from across the whole field of view, which is considerable, hence a large bulbous front element.

Due to the smaller sensor the iPhone lens has a much smaller field of view compared to it's focal length, hence the range of angles the physical aperture has to be visible from is much reduced, allowing the front element, and thus the size of the lens as a whole to be much smaller than the APS-C lens.

Entrance pupil size and front element diameter are extremely well correlated for longer focal lengths, but as you get into ultrawides the correspondence stops. Our 8mm f/4.0 lens should have a tiny front element. The answer is that for a lens to be f/4.0 the physical hole in the lens, that appears to be 2mm wide, must be visible from across the whole field of view, which is considerable; hence a large bulbous front element.

Due to the smaller sensor the iPhone lens has a much smaller field of view compared to its focal length, hence the range of angles the physical aperture has to be visible from is much reduced, allowing the front element (and thus the size of the lens as a whole) to be much smaller than that of the APS-C lens.

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To be precise referred to the entrance pupil, instead of the "physical aperture" (the hole in the lens barrel where the iris is located) as the important factor is not how large the hole is, but how large it appears to be from the outside world. The Canon 600mm f/4 lens has an entrance pupil that is a whopping 150mm wide! Yet it is located in the middle of the lens where there is clearly no space for a 150mm opening.

So you might read from this that a large entrance pupil lens doesn't have to be physically large, however in order for the aperture to appear to be 150mm wide, the opening at the front of the lens has to be at least 150mm. And if you look at it it's clear this is the case.

The answer to this question is that the lens is made from aspherical plastic elements. Asphericals made of glass are very expensive to manufacture, however the iPhone lens is so small they can be moulded from plastic, which is cheap but only works for small elements as the plastic would expand/contract too much on heating when scaled up.

In order to be precise I use the term "entrance pupil", instead of the "physical aperture" (the hole in the lens barrel where the iris is located). The important factor for lens performance is not how large the aperture is, but how large it appears to be from the outside world. The Canon 600mm f/4 lens has an entrance pupil that is a whopping 150mm wide! Yet the aperture itself is located in the middle of the lens where there is clearly no space for a 150mm opening.

So you might read from this that a large entrance pupil lens doesn't have to be physically large, however in order for the aperture to appear to be 150mm wide, the opening at the front of the lens has to be at least 150mm. And if you look at the Canon 600mm f/4 clear this is the case with a dinner plate sized front element!

The answer to this question is that the lens is made from aspherical plastic elements. Asphericals made of glass are very expensive to manufacture, however the iPhone lens is so small they can be molded from plastic, which is cheap but only works for small elements as the plastic would expand/contract too much on heating when scaled up.