Curved Reflections on Water – An Explanation?

    On a recent trip to Canary Wharf with fellow photographers from Tetbury Camera Club for some night photography, we spent some time at Millwall Dock photographing the reflections. When we got home and started processing the images we were looking at curved reflections that seemed to bear no resemblance to what you would expect to see. Here is an example. Some were much more pronounced than this one. Some curved to the left, some to the right.

    Curved Reflection
    Curved Reflection in Millwall Dock, Isle of Dogs

    In searching for reason for these curved reflections there were no plausible explanations on offer until it came up in discussion with Jim who provided an answer after just a few seconds of thought! And after a lot more thought on my part and with the aid of some pencil sketches I came to the conclusion that he is right.

    First of all, this is what it is not…. anything to do with the the lens, or the mirror (mine is a NEX-7 which is mirrorless!).  It is all to do with the reflection of light off the surface of the ripples being blown across the water surface.

    Look at the image above and you will see that the reflections are not representative of the illuminated scene but are reflections of the lightest parts of the scene smeared in a band vertically across the water surface – the obvious examples are the cyan colour of the JP Morgan sign and the purple colour reflected from the horizontal lights on top of the building to right of centre.

    The image above  is an HDR fusion image from individual shots ranging from 0.25 to 15 seconds – some  long exposures. So within the exposure time of the images making up the water we would expect the ripples being blown across the surface to have travelled many centimeters.

    So what is happening. If we take the simple example of waves moving towards the camera and think of a wave as being a mirror we can see how the reflections are smeared by reference to the diagram below. At the point where the wave is flat (A) – at its peak and the bottom of the trough – you should see the normal reflection as if the surface was a mill pond. The leading surface of a wave will reflect light into the camera lens and the trailing surface will also reflect light into the camera lens and here is where the smearing occurs. What I think is happening is that the very bright lights – say the JP Morgan sign – overwhelm everything else above and below. So on the water surface beyond where the reflections of the letters would be for a dead calm surface we see reflections off the leading surface of the ripples (C). And conversely, closer to the camera we see reflections from the trailing surface of the ripples (B). Because the ripples/waves are marching across the water the reflections are merged together and the brightest light dominates. If the ripples are going away from the camera then swap trailing surface for leading surface. The whole effect is accentuated by the long exposure.

    Diagram Smeared Reflections
    Diagram showing how the reflection is smeared by the surface ripples on the water.

    So far so good, but what about the curve? That is explained by the fact that the ripples are not marching directly towards or away from the camera but are at an angle. Depending on the orientation angle of the ripples (which way the wind is blowing), and the position of the camera relative to the subject, the reflection will appear to curve to the left or to the right. So in our case, if my theory is correct, the wind is blowing the waves in a direction that is from near left to far right or far right to near left. Which direction, forward or back, does not matter (just the orientation) but for the sake of this explanation I am assuming far right to near left. In this case the rear edge/surface of the wave is acting as a mirror at an angle and reflects light that should be heading to the left of our camera back into our lens making it appear to come from somewhere to the left of where it should be. And by the same reasoning where we would expect to see a reflection on the right side of the vertical band of light, the rear surface of the ripple reflects the light away from the lens making the water appear dark. If the ripples were orientated far left to near right the reflection would curve to the right.

    Curved Reflection
    Diagram showing how reflection is curved

     

     

    Here is the un-cropped, unprocessed 0.25 second exposure shot with the exposure turned up in Lightroom so you can see what is happening on the surface of the water; and you can see the direction of the ripples on the water surface, running far right to near left as expected.

     

    reflections curved to left
    Reflections curved left showing ripples orientated far right to near left

     

    And below you can see the opposite effect to the one above, with the curves running the opposite way,and the ripples running the opposite way too. QED? I hope so!

    Curved reflections to right
    HDR image of Millwall Dock with reflections curved to the right this time.
    curved reflections
    Here is the shortest  un-cropped exposure of the HDR set with the exposure cranked up in LR to reveal ripples running far left to near right – exactly as predicted.

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Here are my jottings about my photographic projects and activities. I have been working on a focus stacking macro photography rig. There are quite a few posts about that. In addition I write about other photographic activities as and when!

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