Does the size of the front glass mean anything?

Question

Considering the Nikon lenses:

Prime lenses:

• AF Nikkor 14mm f/2.8D ED has a huge front glass (●₃),
• AF-S Nikkor 50mm f/1.8G has a tiny little front glass, deep inside the body (∙₁),
• AF-S VR Nikkor 105mm f/2.8G IF-ED has a tiny little front glass (∙₁),
• AF-S VR Nikkor 200mm f/2G IF-ED has a huge front glass (●₃),
• AF-S Nikkor 300mm f/2.8G ED VR II has a huge front glass (●₃),

Zoom lenses:

• AF-S Nikkor 14-24mm f/2.8G ED has a large front glass (●₃),
• AF-S Nikkor 24-70mm f/2.8G ED front lens is still much larger compared to non-professional lenses of the same range (●₃),

• AF-S Nikkor 70-200mm f/2.8G ED VR II has a large front glass (●₃).

• AF-S DX Nikkor 18-200mm f/3.5-5.6G ED VR II front lens is much smaller than any of the three lenses above, but, well, it's a DX lens (•₂),

• AF-S VR Nikkor 70-300mm f/4.5-5.6G IF-ED front lens is small too compared to the lenses below (•₂),
• AF-S VR Nikkor 24-120mm f/3.5-5.6G IF-ED front lens is again quite small (•₂),
• AF VR Nikkor 80-400mm f/4.5-5.6D ED front lens is pretty small compared to 200mm or 300mm or the 70-200mm (•₂).

I don't see any relation between the size of the front glass and the focal length, focal range or image quality.

If we take only zoom lenses, there would be a link between the maximum aperture and the size of the glass, larger aperture requiring a larger glass. Actually, this is not true, since AF-S Nikkor 17-35mm f/2.8D IF-ED has a large maximum aperture, but a small front glass. Also, this doesn't work at all for prime lenses, where the lens with the largest aperture has the smallest front glass.

The quality of the lens doesn't seem to influence the size of the front glass neither, at least not for the prime lenses.

So what forces to make larger lenses with larger front elements?

Answer

Generally speaking, a larger front element is necessary to achieve a wider maximum aperture. More specifically, a larger front element helps achieve the necessary "entrance pupil" diameter required for a given lens, provides the necessary primary light-gathering power of a lens, and helps achieve the necessary angle of view of the lens. (The entrance pupil is the diameter of the physical aperture as viewed through the front of the lens.)

The physical diameter of a lens generally must increase as the maximum aperture increases, and once you pass f/2.8, each additional stop greatly increases the physical size of the lens. Additionally, once you pass f/2.8, each additional stop requires a considerably greater amount of light, and larger front lens elements are a key factor in gathering that additional light.

For ultra-wide angle lenses, such as the 14mm f/2.8, a larger lens element is often necessary to assist in capturing light rays from a wide enough angle of incidence, more so than for achieving a wide aperture (14/2.8 = 5mm physical aperture, quite small.)

For wider-aperture telephoto lenses, the physical aperture tends to be much larger, which tends to dictate the size of the front lens element more than the necessity of gathering wide-angle incident light rays. The 70-200mm f/2.8 lenses have a physical aperture of 71.4mm, some 14 times larger than the 14mm f/2.8 lens.

Lenses like the 70-300f/4.5-5.6 and 24-120 f/3.5-5.6 have much smaller maximum apertures for their focal lengths. 300/5.6 = 53mm, some 1.5 times smaller for 100mm greater focal length. A 300mm f/2.8 lens would require a 107mm aperture, which is twice as large as a 300 f/5.6, and would require a much larger front lens element to gather enough light to accommodate such a large aperture. The 80-400mm again has a fairly small maximum aperture at its longest focal length...400/5.6 is 71.4mm again, vs. 100mm for the 200/2 and 107mm for the 300/2.8. The 80-400mm lens has a larger front element than say the 14/2.8 or even a 50/1.4 due to the physical size of its aperture...which even at f/5.6 is considerably larger than any wide angle lens. A 50mm f/1.0 lens would have a physical aperture of 50mm, which over 20mm smaller than the 71.4mm of a 400/5.6 lens.

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