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In this photo, why is the sun not positioned exactly above the "axis" from which its reflection seems to spread?

I think it could be how sunlight refracts across the northern hemisphere but I'm not sure. I took this photo and I would be fascinated if this was a physics problem rather than a problem with my camera.

I used an iphone 5s.

From the image you can see that the sun is not positioned exactly above its reflection.

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    $\begingroup$ I dunno but it's kinda weird that the buildings are not perpendicular to the water's surface either imgur.com/a/8Ywdo $\endgroup$
    – pentane
    Commented Aug 6, 2017 at 14:43
  • $\begingroup$ @David Where was the photo taken and what camera and lens did you use? $\endgroup$
    – stardt
    Commented Aug 7, 2017 at 18:57
  • $\begingroup$ @stardt I actually didn't use a camera it was an Iphone 5s and I took it in Hubei, China. $\endgroup$
    – dTdt
    Commented Aug 8, 2017 at 11:04
  • $\begingroup$ Thanks @David. The Iphone 5s has a 4.1 mm focal length lens. Tilting the camera up 7 degrees makes vertical lines lean inward by about 4 degrees at the sides, which matches the photo. I don't have enough reputation to post an answer with the relevant equations. $\endgroup$
    – stardt
    Commented Aug 8, 2017 at 11:41

3 Answers 3

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This is a steal / riff on Asher's correct answer.

If you are using a tablet, tilt it so that the left hand side is closer to your face, now does it look ok, ........on my cheap tablet it does.

No building authority (except Pisa Municipal Council in Italy) would allow this degree of vertical tilt, so obviously the camera does sometimes lie.

This is an example of aberration, caused by distortions of light ray paths inside of the camera lens, particularly with zoom lenses.

This curvilinear aberration can take one of two forms, either like this:

enter image description here

Pincushion distortion:which is what causes the effect in your picture.

Barrel distortion,

Or like this:

enter image description here

These pictures are taken from Curvilinear Distortion.

PhotoSE deals with this, but on first reading anyway, not in as much detail as I would have expected.

I agree, if it was due to a previously unknown aspect of physics, that would be great. Sadly, it's more mundane.

EDIT

In case his comment is deleted, please take account of Samuuel Weir's remark in assessing my wording above:

I don't think that it's a matter of lens distortion. As I recall, it's an apparent distortion primarily due to the fact that the plane of the camera's sensor is tilted upward with respect to the horizon. There are so-called "perspective control" lenses which can correct for the distortion. See, for example: kenrockwell.com/nikon/19mm.htm . Also: en.wikipedia.org/wiki/Tilt–shift_photography (Sorry, it doesn't appear that the entire web address was converted into a hyperlink because of the hyphen. Just copy the whole address and paste it into the address line of your browser

And tfb

I agree with @SamuelWeir I think, although I originally thought the barrel-distortion reasoning was really good: it's more likely to be perspective distortion due to the sensor plane being angled upwards. Although the image is missing any useful EXIF data and the person didn't tell us what camera it was taken with, many modern cameras, if they know enough about their lens will, when creating JPEGS, correct for the distortions they know about. So if this was taken with such a camera, it seems unlikely you'd get so much lens-related distortion.

Both of these users have a much better grasp of physics than I do.

END EDIT

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    $\begingroup$ Well, it is a physics problem, just in a different bit of the system... $\endgroup$
    – user107153
    Commented Aug 6, 2017 at 17:13
  • $\begingroup$ I'm not sure that this is an issue of lens distortion. See my comment above. $\endgroup$
    – user93237
    Commented Aug 6, 2017 at 18:34
  • $\begingroup$ @SamuelWeir Thank you, being realistic, if you are not sure, then I am even less sure. The building distortions, those I think I can justify, but the Sun may be a bit more off line than even barrel distortion can explain. I will edit your comment in to my post? I have no experience of zoom lenses. $\endgroup$
    – user163104
    Commented Aug 6, 2017 at 19:05
  • $\begingroup$ I agree with @SamuelWeir I think, although I originally thought the barrel-distortion reasoning was really good: it's more likely to be perspective distortion due to the sensor plane being angled upwards. Although the image is missing any useful EXIF data and the person didn't tell us what camera it was taken with, many modern cameras, if they know enough about their lens will, when creating JPEGS, correct for the distortions they know about. So if this was taken with such a camera, it seems unlikely you'd get so much lens-related distortion. $\endgroup$
    – user107153
    Commented Aug 6, 2017 at 19:17
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    $\begingroup$ Seriously: it was (and is) a great answer! $\endgroup$
    – user107153
    Commented Aug 6, 2017 at 21:47
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This appears to be a problem of perspective, which has resulted from tilting the camera upward (as evidenced by the low position of the horizon). Notice that the buildings on the left of the frame tilt to the right, and the buildings on the right of the frame tilt left. If you draw a line along the center if the reflection, it lines up with the sun well enough.

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  • $\begingroup$ Tilting my tablet away from me on one side,. ( that is bringing the l .h.s closer to my face, ) sorts it out +1 $\endgroup$
    – user163104
    Commented Aug 6, 2017 at 20:56
  • $\begingroup$ The camera is barely tilted upwards at all: the viewpoint can't be below the water and the opposite shoreline is only slightly below-centre. The angle of tilt can't be more than a degree or two and that wouldn't cause the significant tilt that's visible on the buildings. $\endgroup$
    – David Richerby
    Commented Aug 7, 2017 at 7:22
  • $\begingroup$ @DavidRicherby the horizon sits at about 1/3 up from the bottom of the frame, or 1/6 below center. If you assume a 30° field of view, that's 5° tilt already. This seems to be a wide-angle shot so I'd hazard that the FOV is closer to 60° and the tilt thus about 10°. $\endgroup$
    – Asher
    Commented Aug 7, 2017 at 16:34
  • $\begingroup$ @Asher The sun's diameter is about 0.5 degrees and covers 200px, so the view is tilted up by about 1 degree. The field of view is then 8 by 6 degrees, roughly equivalent to a 260 mm lens on a 35 mm camera. See my annotated photo. A 1 degree tilt would make a building at either edge of the photo "lean" in by less than 0.1 degrees, not ~4 degrees. It's probably distortion. $\endgroup$
    – stardt
    Commented Aug 7, 2017 at 18:57
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    $\begingroup$ @Countto10 I think we've each explained half of a complete answer. That is to say, if your answer were expanded with a section almost just like my answer (after all, you wouldn't want to plagiarize, right?) it would be both correct and complete and there's nothing I could do to stop you wink wink $\endgroup$
    – Asher
    Commented Aug 7, 2017 at 23:38
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In your case, it looks like a camera effect explained in other answers.

However...

You can see this effect with just your naked eye on a lake on a windy day. The average angle of the water's surface changes from flat-on-average to slightly-tilted-on-average because of the wind. This means that the apparent position of the center of the "mirror" that reflects the sun's light into your eyes shifts from directly under the sun to some place slightly off to one side. A flat calm surface would give you an image of the sun only. A wobbly surface which was flat on average would give you a dappled bright spot that's larger than the sun's image is alone and stretched out towards you a bit. Add some wind, and the bright spot grows larger and it's average position appears to shift to one side.

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