snell: Calculate the refraction angle
In AlexCast/rho: R Hydrology Optics

Description Usage Arguments Details Value References See Also Examples

The function calculates the (complex) angle of refraction for eletromagnetic radiation transmitted to a medium.

1	snell(thetai, ni, nr)

`thetai`	Incidence angle relative to the normal of the interface between the two mediums (radians).
`ni`	Refractive index of the medium of incidence (unitless).
`nr`	Refractive index of the medium of refraction (unitless).

The angle of incidence is limited to be between 0 and pi/2. Although the sine function is periodical and the modulus will be correct for multiples of a given angle, this serves as a protection in case incidence angles > pi/2 are inadvertently provided. NAs are allowed in all arguments.

The indexes of refraction may be complex numbers. If so, the function will return the complex refraction angle. This complex refractive angle should be passed to the fresnel function to calculate the reflectance at the interface with an absorptive medium. Complex refractive angles can be converted to angles of constant phase or constant amplitude with the appropriate function (snell_decomp). Note that the refractive indexes are normalized to each other internally, so if passing refractive indexes that are already relative, one of the refractive indexes should be equal unity. See examples.

If one of the mediums have a negative refractive index, the refracted ray will occur on the same side of the normal as the incident ray, i.e., the azimuth is rotated 180° to that of the incident ray. Since this is a special condition not occurring for hydrological optics, the functions are simplified by requiring that the refractive indexes be positive.

For real indexes of refraction, in case of incidence angle is higher than the critical angle for total internal reflection (thetai > asin(nr / ni)), the function will return a real refraction angle of pi/2, i.e., absence of refraction.

A numeric or complex vector.

Bohren, C. F.; Huffman, D. R. 1983. Absorption and Scattering of Light by Small Particles. Wiley, New York.

snell_decomp, fresnel

# Refraction from standard dry air to average seawater at 550 nm:
snell(c(0, pi/4, pi/2), ni = 1.000278, nr = 1.342033)

# Same as before but seawater index already relative to air:
snell(c(0, pi/4, pi/2), ni = 1, nr = 1.342033 / 1.000278)

# Same as before, but reversed direction:
snell(c(0, pi/4, pi/2), ni = 1.342033 / 1.000278, nr = 1)

# Same as before, but with the complex index of refraction of water:
snell(c(0, pi/4, pi/2), ni = complex(real = 1.342033, imaginary = 2.442E-09) 
      / 1.000278, nr = 1)