Ever wondered why a lake appears so much darker when viewed directly but then changes into a mirror at a shallow angle, or why shiny surfaces happen to be so much brighter at some view positions? These can be explained by applying the very basic notion of Fresnel reflection in optics that helps explain how light interacts with different interfaces.
What is Fresnel Reflection?
Named after French physicist Augustin-Jean Fresnel, Fresnel reflection describes the dependence of the amount of reflected light upon the angle under which the surface is viewed. The fact forms the very basis of everything from everyday optical effects through to state-of-the-art applications in computer graphics and materials science.
The Science Behind the Effect
Actually, most ways in which light interacts with surfaces are controlled by some pretty complicated physical laws. Wherever light hits a surface, all sorts of possible interactions are happening: it involves a portion that reflects from the surface, another part of light travels through-transmission-but yet another part may get really absorbed and converted to heat. Developed in the early 1800s, the Fresnel equations describe the exact balance of these. These equations represent, mathematically, the amount of the light will be reflected versus transmitted for a given angle; the variation with viewing angle is very extreme in these proportions.
The Grazing Angle Phenomenon
The most interesting feature of Fresnel reflection occurs for grazing angles—the so-called glancing angles at which one views a surface from very low down. Most reflective surfaces reflect just 2 to 5 percent of incident light if viewed directly from above. If you look at a surface from an increasingly shallower angle, however, the reflected portion grows extremely rapidly. At very shallow angles, say around 80 to 90 degrees, almost all surfaces turn into brilliant, shiny mirrors. It has explained why more shiny-like water bodies are perceived at a distance and why shiny floors seem to radiate brightness when perceived from a distance.
Change of the reflectivity amount of water dependending on the angle you are looking at the water
Mathematical model
The mathematical foundation of Fresnel reflection lies in the Fresnel equations. Although the complete derivation involves some complex electromagnetic theory, the essentials can be understood by some simpler relationships. The Fresnel equations take two general forms; one for light polarized parallel $(r_{\parallel})$ and one for light polarized perpendicular $(r_{\perp})$ to the plane of incidence:
Fresnel Reflection Equations
For parallel polarization (\(r_{\parallel}\)):
$$ r_{\parallel} = \left( \frac{n_2 \cos \theta_i – n_1 \cos \theta_t}{n_2 \cos \theta_i + n_1 \cos \theta_t} \right)^2 $$
For perpendicular polarization (\(r_{\perp}\)):
$$ r_{\perp} = \left( \frac{n_1 \cos \theta_i – n_2 \cos \theta_t}{n_1 \cos \theta_i + n_2 \cos \theta_t} \right)^2 $$
In this equations; n₁ is the refractive index of the first medium (often air, n₁ ≈ 1.0) n₂ is the refractive index of the second medium θᵢ is the angle of incidence θₜ is the angle of transmission.
For unpolarized light (most natural light), the reflection coefficient R is the average of these two components:
$$ R = \frac{r_{\parallel} + r_{\perp}}{2} $$
The angle of transmission $\theta_t$ can be found using Snell’s law:
$$n_1 \sin \theta_i = n_2 \sin \theta_t$$
In most computer graphics applications, however, it employs a popular approximation called Schlick’s approximation, which gives an efficient way of computing Fresnel reflection.
$$R(\theta) = R_0 + (1 – R_0)(1 – \cos \theta)^5$$
Where $R_0$ is the reflection coefficient at normal incidence :
$$R_0 = \left( \frac{n_1 – n_2}{n_1 + n_2} \right)^2$$
The dramatic increase in reflection at grazing angles is a direct consequence of the mathematical behavior of these equations, not just a qualitative observation. For most common materials, the reflection coefficient approaches 1 (total reflection) as the angle of incidence approaches 90 degrees. The refractive index difference between materials determines the minimum reflection at normal incidence. This explains why a glass-air interface (n₂ ≈ 1.5) reflects more light than a water-air interface (n₂ ≈ 1.33) when viewed straight on.
You could use our fresnel reflection calculator to calculate refraction angle, power transmissivity for both polarization and for unpolarized light.
Real-World Applications
Fresnel reflection has changed absolutely many industries. Among the wide uses, it has found its place to let 3D artists and game developers create absolutely realistic materials in computer graphics and video games. Indeed, modern rendering engines have taken the Fresnel equation to model precise light interactions with given surfaces and enhance the virtual environments as never before.
These are great principles in architecture and design when it comes to glass building constructions and glass lighting solutions.
Architects can also predict and control better how their structure will interact with natural light at different times of the day. This understanding has also contributed toward a much-improved efficiency of solar panels due to better controlling light reflection and absorption.
Fresnel reflection has greatly aided photography and filmmaking due to a good understanding of it. Photographers use special polarizing filters which control these reflections so that the scene is captured precisely as they see it. As for cinematographers, they use such an effect toward creating the right mood or atmosphere of a shot, adding depth and dimension to their visual narration.
Common Examples in Daily Life
Water surfaces perhaps provide the most dramatic example of Fresnel reflection in nature. On lakes and pools, it is quite spectacular at any time while the sun is low, transforming them into brilliant reflective surfaces.
Glass windows of buildings show similar characteristics, appearing more like mirrors when viewed at shallow angles-a very important aspect concerning the design of buildings and privacy issues.
Its wide application can be found in car paint design in the automotive industry.
That glitter of car paint, which apparently changes at every angle, does not come by accident but is, as a matter of fact, a very well-engineered feature, laying on such optics to result in much more visually appealing vehicles.
Photography and Artistic Considerations
This knowledge of Fresnel reflection may be used to great advantage by professional photographers and artists in enhancing their works. With great sensitivity to viewing angles and an appropriate set of polarizing filters, unwanted reflections can be eliminated or specially enhanced as a creative effect. This knowledge brings many new openings for subtle decisions in composition and thus boosts the quality within the visual artistry produced across media.
Conclusion
Fresnel reflection represents more than just a scientific term, it’s a fundamental principle that shapes our visual world. From the simple beauty of a lake’s surface to the cutting-edge development of virtual reality environments, this principle of physics continue to influence how we see and interact with our surroundings. By understanding Fresnel reflection, we gain a deeper appreciation for the complex interplay between light and matter that creates the visual richness of our world.
Did you know?
– Ancient Roman glassmakers unknowingly utilized Fresnel reflection principles in creating their famous dichroic glass, which appears to change color depending on the viewing angle. The most famous example is the Lycurgus Cup from the 4th century AD, which appears green in reflected light but red in transmitted light.
– A lot of special effects in the film industry find application with the Fresnel reflection formula. The underwater shoot is filmed with special equipment and light angles by the cinematographer, calculated using Fresnel’s equations, which would help to reduce unwanted reflections and yield clear footage underwater.
-More recently, some new building designs have employed special coatings in their designs to fool Fresnel reflection into making windows virtually invisible at selected angles. This is achieved with prudent matching of refractive indices so that at particular view angles, the Fresnel reflection will be minimized.
-The brilliance of diamond is partly due to Fresnel reflection. Because diamond has a high refractive index of 2.417, Fresnel reflection occurs much more strongly than in most other gemstones, giving it more luster. This is why diamond appears duller when greasy or underwater. Water or grease reduces the contrast in refractive index between the diamond and its surroundings.
-Iridescent colors of butterfly wings arise in part because of Fresnel reflection, besides its combination with other optical effects. Complex reflection over microscopic scales depending on the angle of view gives the wings the characteristic shimmer.
– Engineers and physicists developed camouflage methodologies using the principles of Fresnel reflection throughout the Second World War; they engineered materials and coatings that reduce reflection at certain angles, making vehicles and equipment less observable from an aerial perspective.
