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Clearly, a lens with focal length F and aperture 1/f has to be at least F/f mm wide. Maybe a little more to accommodate the angle of view.

However, lenses tend to have wider front elements than F/f. For example, my Sony 24-240 3.5-6.3 has filter thread 72 mm, and the front element is not much smaller than that. But, 240/6.3=39, so it would seem that, theoretically speaking, the front element shouldn't have to be much wider than 39 mm, if one would account only for F/f.

Is there another physical reason for that?

Michael C
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Michael
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1 Answers1

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Lenses with very narrow angles of view require front elements that are roughly equivalent to the size of the entrance pupil. A typical telephoto prime lens will have a front element less than 10% larger than the entrance pupil at the lens' maximum aperture. This is because the light rays collected by the lens are almost perpendicular to the imaging plane and the entrance pupil will not be much larger than the diameter of the front element.

But with wider angles of view and their closer subject distances, the entrance pupil can be much larger than the front element:

A simple single element lens:

enter image description here

A multiple element compound lens:

enter image description here

If the front element of a wider angle lens were only large enough for the entrance pupil to be fully visible from subjects centered on the lens' optical axis, the lens would severely vignette the light coming from the off axis portions of the frame. Thus wide angle lenses tend to have much larger front elements than the size of the entrance pupil so that a larger portion of the entrance pupil is visible from the more peripheral parts of the field of view.

When portions of the lens' field of view are obstructed from a full view of the entrance pupil, it can result in dark corners and oddly shaped out of focus highlights. Consider wide aperture lenses with even a normal field of view:

enter image description here

Such a lens is said to have "cat's eye" bokeh:

enter image description here

Even when there is no mechanical vignetting caused by the lens barrel, from wider angles the entrance pupil appears to be an oblong shape, rather than a circle.

enter image description here

Compare these examples, all intended for full frame cameras:

  • Canon EF 300mm f/4 has 77mm filter threads. 300mm/4 is 75mm
  • Canon EF 100mm f/2 has 58mm filter threads. 100mm/2 is 50mm
  • Canon EF 85mm f/1.8 has 58mm filter threads. 85/1.8 is 47mm
  • Canon EF 50mm f/1.4 has 58mm filter threads. 50mm/1.4 is 36mm
  • Canon EF 35mm f/2 has 67mm filter threads. 35/2 is 17 mm
  • Canon EF 24mm f/1.4 has 77mm filter threads. 24mm/1.4 is 17mm

Your 24-240mm f/3.5-6.3 lens having a near 72mm wide front element probably is more about reducing vignetting at 24mm and f/3.5 than it is about the needed entrance pupil for 240mm and f/6.3.

Michael C
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  • Ahhh, "cat's eye bokeh" is what it's called. Also very prominent on the Canon 50mm f1.4 SSC IIRC... – rackandboneman Jan 26 '19 at 22:16
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    Maybe it's just me, but I'm still trying to figure out how "the entrance pupil can be much larger than the front element". It can (and usually is) certainly be much larger than the actual physical diaphragm, but a virtual image that goes outside the physical boundary of the front element...? – twalberg Mar 23 '19 at 13:12
  • @twalberg What is it about the first diagram in the answer above that is not self evident? This diagram shows two additional dotted lines that show why the entrance pupil is the distance it is behind the lens. The entrance pupil is viewed through the front of the lens from a point on the lens' optical axis at the focus distance, but the aperture opening appears to be a certain distance behind the front element, not on its surface. – Michael C Mar 23 '19 at 17:52
  • This is why wide angle lenses often (almost always) have much larger elements that required by the size of their e.p. - to prevent vignetting because the entire e.p. would not be visible from the edges of the lens' maximum AoV. But they don't have to be that large if light fall off on the edges is not a concern. – Michael C Mar 23 '19 at 18:05
  • @MichaelC That doesn't answer my question. How can an entrance pupil, which is admittedly a virtual image, appear larger than the physical limits of the front lens element? Viewing from on-axis at any point, before, at or behind the focus distance, the entrance pupil must fit within the confines of the front element, otherwise light must be required to pass through the opaque portions of the lens outside the physical boundaries of the front element. – twalberg Mar 23 '19 at 18:14
  • @twalberg Because the e.p. always appears to be behind the front lens element, in the same way that looking from the back of a lens through the front does not limit the field of view to the size of the front element of the lens, only in reverse. Lines drawn from a point to the two sides of an opening with real thickness form an angle. That angle continues in a cone of ever increasing size. It should be perfectly clear by looking at the diagram above, or by looking through a cardboard tube only an inch or two in diameter and being able to see an entire house in the distance. – Michael C Mar 23 '19 at 18:26
  • "The entrance pupil is the size of the physical aperture that would be required to pass the extreme ray if the lens was not present." The refractive properties of the lens make the light coming from the edge of the physical aperture, when viewed from the lens' optical axis, appear to be located on the dotted lines that continue along the line formed by the extreme rays that are allowed to pass through the physical aperture. – Michael C Mar 23 '19 at 18:31
  • http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/stop.html – Michael C Mar 23 '19 at 18:33
  • From the above link: "The entrance pupil is defined as the image of the aperture stop as seen from an axial point on the object through those elements of the lens which precede the stop." The angle/field of view is the range of non-axial points from which some portion of the entrance pupil is vislble, and can definitely be larger than the front element. But viewed from the lens' axis, the entrance pupil cannot extend outside the physical boundaries of the lens' front element. How can you look at a lens straight on and see an image of the aperture that is bigger than the lens? – twalberg Mar 24 '19 at 01:20
  • Yes, the entrance pupil size is sufficient to admit those extreme rays, but from an axial view, those extreme rays do not form a part of the image that is the entrance pupil. – twalberg Mar 24 '19 at 01:25
  • "How can you look at a lens straight on and see an image of the aperture that is bigger than the lens?" Because it is in a larger part of the cone behind it. It is plain as day on the first diagram above. You don't "see" the aperture stop where it is behind the lens. You "see" the aperture stop after it has been refracted by the lens and appears to be behind the aperture stop and larger than the spread of the maximum rays where they enter the front of the lens. – Michael C Mar 24 '19 at 01:28
  • Our lens need no extend all off the way to a pretty tip. All of the lens outside the maximum rays are superfluous and are not required to be there. Most front elements are "chopped off" on the ends in this way. Look at this diagram. If we are observing from point O, the entrance pupil appears much wider than any of the lens elements because the light going through them is being refracted. – Michael C Mar 24 '19 at 01:35
  • The "tube" we are looking into appears larger than the external tube that contains it because the view from inside is being magnified by the lenses between the front of the len and the aperture stop. It is no different than looking in a box with a small circle cut in the side and seeing a piece of the other side of the inside of the box that is larger than our circle. The closer we are to the box, the larger the ratio between the circle we can see compared to the circle we are looking through. – Michael C Mar 24 '19 at 01:41
  • Here's a color annotated version. The red lines are the maximal rays. When observed from point 'O', the entrance pupil will appear to be the length of the green line away from point 'O' with a width of the blue line. – Michael C Mar 24 '19 at 02:01