According to Snell's law and Fresnel's equations, using IOR of 1.33 for water, my calculation of Fresnel's suggest the reflectivity of water at an angle of incidence of 0 is approx 0.02 (i.e. 2%). Googling turned up multiple references that quoted the same figure (suggesting my calculations are probably correct - or else multiple people are making the same mistakes that I am!).

As I understand it, that means that looking straight down (e.g. from a bridge) onto a calm water surface, my eyes should only see 2% of the light versus if I were standing in the water looking up.

That seems dark enough that I would never be able to see anything when looking down - not myself, not the bridge, but not the sky either - unless (perhaps) I wore blinkers, enabling my eyes to adjust to the extremely low (50x lower than surroundings!) light levels.

And yet ... I can clearly see the outline of myself versus sky.

I couldn't find a convenient bridge, but ... last week I went out with a camera and took photos of calm water at different angles on a sunny day. Experimentally, at angle-of-incidence of approx 60 degrees, reflections are bright, easy to distinguish fine detail in shadows of what's reflected, and fully coloured. My calculations of the Fresnel equations suggest this should be at approximately 5% (20x reduction in light).

My first thought is that I need to more accurately measure the angles with the camera (I've been judging by eye), but ... I'm afraid that my Fresnel calculations are woefully wrong. Or ... can we really see 50x loss in light, without blocking out surrounding light sources? I thought the eye wasn't that sensitive unless it could readjust to low-light conditions?


1 Answer 1


The eye is an extremely nonlinear brightness meter. A well-lit room is about $10^{-2}$ as bright as sunlight. Moonlight is about $10^{-6}$ as bright as sunlight. In general our senses tend to act more logarithmic than linear.

  • $\begingroup$ But we don't simultaneously see the whole range of brightness, right? I thought that e.g. Moonlit items are pure black to us if viewed from a sunlit environment. Whether the eye is capable of perceiving something in isolation is a separate question, what I'm wondering / confused by is: the eye is capable of perceiving both extremes at once? $\endgroup$
    – Adam
    Nov 7, 2019 at 12:29
  • $\begingroup$ @Adam: What you say is true, but 0.02 is not an extreme ratio like $10^{-6}$. $\endgroup$
    – user4552
    Nov 8, 2019 at 4:32

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