# Why is the front element of a telephoto lens larger than a wide angle lens?

A wide angle lens has a wide angle of view, therefore it would make sense that the front of the lens would also be wide. A telephoto lens has a narrow angle of view, so it would make sense that the angle would be smaller. However, this is the opposite of what one can see on real lenses.

Why is this the case?

That is a generalization that is not always true.

The front element is not only sized to accommodate the field-of-view but also for the maximum aperture. Since aperture is measured as a fraction of focal-length, a longer lens requires a physically larger aperture to reach the same F-stop.

For example:

• The Nikkor 200mm F/2 lens requires an aperture 100mm across and you can see from the spec that the lens diameter is 124mm.
• The Nikkor 35mm F/2 lens requires an aperture 17.5mm across and you see that the diameter of lens is much smaller.
• The Nikkor 300mm F/4 lens requires an aperture 75mm across, so although it is longer than the 200mm F/2, does not need to have such a large front element and its diameter is 90mm.
• The Nikkor 14-24mm F/2.8 is an ultra-wide lens with a diameter of 98mm although its aperture only needs to be 8.6mm across (24/2.8) but it ends up much wider to accommodate the field-of-view.

The size of the front lens element is not specifically related to the lenses angle of view, although that is a factor. That is more a function of the curvature of the front lens element, as a greater curve is what increases the angle of incident light that can be captured and bent by the lens. The diameter of the front lens element is more indicative of the "speed" of a lens, its maximum aperture. As lenses are rated in relative aperture these days, such as f/4, that means the longer the focal length (f), the wider the lens tube must be to accommodate a similar aperture as a wide angle lens.

If we take two lenses, one wide and one long, that have an f/4 aperture. One lens is 16mm, the other is 400mm. The apparent maximum aperture, or `entrance pupil diameter`, is the size of the aperture as viewed through the front lens element. The pupil diameter must be 4mm for the wide angle lens, but 100mm for the long lens, at an f# (N) of 4. Assuming we had an f/2.8 lens, the wide angle would have a pupil diameter of 5.71mm, while the long lens would have to have a pupil diameter of 143mm.

When it comes to telephoto lenses, the picture gets a bit muddier. If you have ever used an actual 400mm prime, or 100-400mm/80-400mm zoom telephoto lens (which tend to have an f/5.6 or 71mm maximum aperture), you should know that the front lens elements are not actually 71mm in diameter. In the contrary, they are probably closer to 60-70mm in diameter, meaning it is impossible for the entrance pupil to appear as large as it should according to the f-number in any case. (The aperture will usually appear quite a bit smaller than the front lens element when viewed through the front of the lens.) The construction of telephoto lenses is rather complex, as they use back-focusing groups to allow the lens to be a different length than the focal length. Generally speaking though, the reason a telephoto lens has larger front lens elements is pretty much the same...a larger aperture requires a larger lens tube diameter, therefor requiring large front lens elements.

(NOTE: The last paragraph is based on actual observations with the Canon EF 100-400mm f/4.5-5.6 L series lens at 400mm. This lens has a 77mm filter thread, and the front lens element has an actual [roughly measured] diameter of about 62-63mm. At f/5.6, the 400mm focal length would dictate a 71mm entrance pupil diameter. Given that the front lens element is at most 63mm, and the entrance pupil diameter as viewed through the front of the lens is smaller than that (as you peer down a tube, due to perspective, the diameter shrinks the farther down the tube you look), it is impossible for the apparent aperture size at f/5.6 and 400mm to be as large as it "should be" if you simply calculate the number as `focal length \ f-number`. Its difficult to get any kind of accurate measurement, but it appears to be about 22-25mm as viewed through the front of the lens.

In contrast, it should also be noted that in the case of the Canon 16-35mm f/2.8 L series lens, at 16mm, when the maximum aperture is viewed through the front of the lens and measured with a ruler, does appear to be just shy of 6mm, which is exactly how it should appear given an f/2.8 aperture, which should be exactly 5.71mm. This observed difference between the apparent size of the aperture of a wide-angle lens vs. a telephoto lens gives rise to my opinion that the specialized construction of a telephoto lens has an impact on the apparent aperture size, allowing it to be smaller than it "should be" according to the f-number.)

• The last paragraph seems confusing. I don't think there are any 100-400 or 80-400 lenses that claim to be f/4 at 400 mm. Could you bring an example of 400mm f/4 with front element less than 100mm? Both Canon and Pentax seem to be larger than 100mm. – Imre Jun 23 '11 at 5:16
• @Imre: Well, true, zoom lenses up to 400mm are usually f/5.6. That is still a 71mm aperture diameter. I have the Canon 100-400mm lens, which has a 77mm filter diameter and the front lens element is about 62mm in diameter. The apparent size of the aperture is quite a bit smaller than the front lens element when you look through the front of the lens, so its certainly not 71mm in either physical or apparent size. – jrista Jun 23 '11 at 6:18
• It should also be noted that the full tube diameter is not completely "available" for aperture diameter. You have the thickness of the tube body itself, a fair bit of mechanics and electronics plastered around the inside of the lens, along with lens element mounts as well. The diaphragm has its own mount, as well as the ring and mechanism that holds the diaphragm blades. In the case of the Canon 100-400mm lens, the full outer tube diameter is 92mm, with a narrower inner tube (its a push-pull design, and I measured the diameter of the inner tube, where the diaphragm is, at about 78mm). – jrista Jun 23 '11 at 6:39
• The inner tube diameter only matters around front element because behind front element, the light rays are already bent and take less room than the full aperture. I suspect the smaller-than-required front element (giving a mere f/6.3, missing third a stop) might be a case of manufacturer lying, meaning only that thanks to low losses in quality glass exposure is similar to what you could expect from f/5.6. – Imre Jun 23 '11 at 9:02
• @jrista I disagree that telephoto construction has anything to do with the apparent size of the aperture. The reason longer lenses need larger apertures for the same f/stop is because they're looking at a smaller area of the scene. Any 200mm lens, telephoto or not, will see the same field of view, so will need the same apparent aperture size to capture the same amount of light. – Evan Krall Jun 23 '11 at 14:10

To put it quite simply, and avoiding technical concepts, a wide angle lens simply takes in more light than a telephoto. Imagine a picture taken at 50mm and 100mm. The 100mm will produce an image that will only show 1/4 of the image of the 50mm (half the image on each side).

Then consider the light that reaches the lens. That light originates from the objects that you see on the image. As the image taken at 100mm only contains 1/4 of the image, only 1/4 of the light will reach the lens.

Therefore the longer focal length will need to have a larger front element in order to take in more light in order to be able to get a properly exposed image.

In the case of a really wide-angle lens, you're right: the front element is extremely large to accommodate the large angle of view. For an extreme example, consider the 6mm Nikkor.

When the angle of view is less than 180 degrees, the front element can (does) shrink pretty quickly though. Even so, many wide-angle lenses have a front element that's extremely rounded, often sticking out far enough that you can't use a filter with them.