As mentioned in the Maxwell Materials page, the Nd is the index of refraction of the material. The name Nd is used because it is the common way to denote an index of refraction that has been measured at the wavelength of 589.3 nm for a certain material. You can find a list of common IOR values here. The Nd is important not only for transparent materials but for all materials as it defines both surface reflections and the refraction of light inside the object.
The Fresnel Effect
Before explaining how Nd influences the look of a material, it is important to understand the “Fresnel effect”, named after the french physicist who first described it. This effect states that the strength of reflections on a surface is dependent on the viewing angle. For example, if you look straight on at your monitor screen, you will see very weak reflections, but if you look at the screen at an angle, the reflections will appear stronger. With a higher Nd number the surface will start to look equally reflective, no matter the viewing angle. So in effect, a higher Nd “weakens” the Fresnel effect.
The same plastic material above with Nd 1.1 (left) and Nd 1.6 (right). The resulting "fresnel curve" flattens out as the ND increases, making the surface equally reflective from all viewing angles.
Nd and Reflectance 0/90
Changes in the Nd number affect the overall reflectivity of an object. For example, you can have the Reflectance 90° color set to full white, but with an Nd of 1 the object will have very weak reflections. Setting the Nd to a high value like 40 and keeping the Reflectance 90° to that same full white color will result in a mirror-like surface. The following images demonstrate this:
Reflectance 90 white with Nd=1 (left) compared with Reflectance 90 white with ND=40
From the images above you can see that raising the Nd increases the effect of the Reflectance 90° color, while the Reflectance 0° color (in this case set to nearly black) has less and less effect when increasing the Nd. Of course the value of the Reflectance 90º color will also affect the maximum strength of reflectance. For example, you can set a high Nd but set the Reflectance 90° to a dark color. The result will be a surface which is reflecting equally, no matter the viewing angle, but the reflections will appear weaker.
For opaque shiny materials (low roughness), an Nd of at least 3 is recommended if you want them to be overall reflective (no Fresnel falloff). To mimic a metallic material the Nd needs to be even higher. The Nd setting can go as high as 1000. For a mirror-like surface it is usually enough to set the Nd to 100.
The amount of light that is reflected back from the object is determined by the refl 0° and 90° colors. The Nd controls the Fresnel curve, or the influence of these two colors, depending on viewing angle. In reality however, the Nd itself specifies how much light is reflected back from the surface, with a higher Nd specifying a more reflective material. These three settings (refl0°, refl90°, Nd) can come into conflict when you put in, for example, a black refl 0° color but a very high Nd. Force Fresnel ensures that the reflectance ramp (curve) between Ref0 and Ref90 will be maintained by the given Nd. It discards the luminance of a given reflectance color and enforces physically correct Fresnel while only deriving the hues of the refl. 0° and refl. 90° color chips.
When Force Fresnel is unchecked the reflectance value of a surface is derived both from the Nd and the luminance of the refl0° color. When Force Fresnel is checked, the reflectance between refl0 and 90° (the Fresnel curve) is maintained according to the Nd, and only the hue of a given reflectance color is taken in consideration.
This option should be turned off when you texture the refl. 0° or refl.90° channels, otherwise your textures may not appear as you expect when using a lower roughness. As you can see in the images below, because the luminance information of a given color is discarded, a bright red in your texture may appear darker than expected if the Nd is low and the Force Fresnel option is checked. Here, Maxwell Render is determining the final reflectance of the object, just looking at the Nd.
Nd=30 (left) and ND=30 with Forced Fresnel(right)
Another example with Nd=30 (left) and ND=30 with Forced Fresnel (right)
You should turn on Force Fresnel when you are working with untextured refl. 0° and refl.90° channels to create more realistic metals or other shiny materials. Force Fresnel will then ensure a correct reflectance across the entire surface, even if you set a very dark refl. 0° color.
Nd and Roughness
The Nd has no influence on the look of the material when working with Lambertian materials. Lambertian is a special mode which makes a surface reflect all light in a diffuse way (its roughness is 100). It is the highest roughness a surface can have. It is also important to remember that the Nd has less influence on the reflectance of an object the higher you set the Roughness and instead it's the Reflectance colors that matter more and more. You will see the biggest changes to the reflectiveness of the object as you change the Nd, when the surface roughness is low.
From a physical point of view, the index of refraction is not just a plain number. In fact it is a number derived from a complex calculation to define the refractive index at one particular wavelength. This is the calculation:
Refraction at a particular wavelenght = Nd + K.i
The Nd represents the refractive index, which is the well-know concept of Index of Refraction we often use.
The K is the extinction coefficient: the amount of absorption loss when an electromagnetic wave propagates through a material. This is usually confused with the Abbe, but it is not related to this. K is related to the extinction of the wave.
The use of the K value is optional. In most situations it is enough to just use the Nd value. Only in specific situations where the extinction effect is important, is it necessary to use the K parameter to get a more precise result.
The values of the extinction coefficients are obtained from measurements in laboratory, and are also included in the IOR files.