If you've looked at a body of water under sunlight, you might have noticed that the water looks transparent close to you, but looks like a mirror further away. This is because the fraction of light that is reflected at an interface between two media depends on the angle of incidence; the nearby water is viewed at a steeper angle, so relatively more light is transmitted. The exact relationship is described by the *Fresnel equations*. ("Fresnel" is pronounced fruh-nell) There are four equations describing reflected and transmitted amplitudes for each of the two polarizations of light (*s-* and *p-polarization*). It's not important for our purposes what the difference between these kinds of polarization is; daylight is unpolarized, so in this case it's safe to just average the two. We have two equations for the reflected amplitude, where the subscript on $r$ denotes the polarization, $\theta_i$ is the angle of incidence, $\theta_t$ is the transmission angle (determined from Snell's law), and $n_1, n_2$ are the refractive indices: $ r_s = \frac{n_1 \cos \theta_i - n_2 \cos \theta_t}{n_1 \cos \theta_i + n_2 \cos \theta_t} $ $ r_p = \frac{n_1 \cos \theta_t - n_2 \cos \theta_i}{n_2 \cos \theta_i + n_1 \cos \theta_t} $ These are slightly different from the results presented [on Wikipedia](https://en.wikipedia.org/wiki/Fresnel_equations); the second one is negated. I am pretty sure that there is an error on Wikipedia, both because [these lecture notes](https://www.brown.edu/research/labs/mittleman/sites/brown.edu.research.labs.mittleman/files/uploads/lecture13_0.pdf) present the version above and my [[Soap films|soap film simulator]] gave the wrong results when using Wikipedia's version. The transmitted amplitudes can be computed from the reflected amplitudes: $ t_s = r_s + 1 $ $ t_p = \frac{n_1}{n_2} (r_p + 1) $ Note that these are *amplitudes*, and need to be squared to produce values for the light's intensity. Plugging in values will reveal that water (refractive index 1.33) is considerably more reflective at shallow angles.