What is specular reflection?

Specular reflection is a phenomenon that occurs when light interacts with a smooth and shiny surface, such as a mirror or a polished metal. The behavior of the specular reflection can be described by considering the interaction between the incident light waves and the surface. The incident light is reflected in a single but opposite outgoing direction.

Reflections on still water are a good example of specular reflection.

The law of reflection

The law of reflection is a fundamental principle in optics that describes how the light behaves when it encounters a reflective surface.

Specular reflection follows the law of reflection which states that the incident ray ($i$), the reflected ray ($r$), and the normalA line perpendicular to the surface. ($n$) all lie in the same plane.

The angle of incidence ($\theta_i$) is equal to the angle of reflection ($\theta_r$).

The law of reflection can be represented as follows.

Where,

• $\theta_i$ is the angle of incidence, which is the angle between the incident ray and the normal at the point of incidence.

• $\theta_r$ is the angle of reflection, which is the angle between the reflected ray and the normal at the point of incidence.

Note: If the light wave strikes the smooth surface at a $45^\circ$ angle relative to the surface normal, it will be reflected at an angle of $45^\circ$ to the other side of the normal.

Such reflection of light allows for the formation of clear and sharp images in specular reflection.

Specular reflection can be calculated as follows.

Where,

• $I_{\text{spec}}$ is the intensity of the specular reflection.

• $k_s$ is the specular reflection coefficient to determine how strong or weak the specular reflection appears.

• $I_l$ is the brightness of the light source illuminating the surface.

• $\mathbf{e} \cdot \mathbf{r}$ is the angle between the observer's line of view and the direction of the reflected light.

• $\max(0, \mathbf{e} \cdot \mathbf{r})^p$ controls the size and sharpness of the specular highlight, making it more or less focused depending on the value of $p$. We use the max function to not compute the specular reflection for surfaces facing away from the user. The dot product of two such vectors where the angle is greater than or equal to $90 \degree$is negative. Hence the specular reflection for such surfaces will be $0$.

• $p$ is the surface shining constant.

  • Dull surfaces have small values of $p$.

  • Shiny surfaces have large values of $p$.

The angle ($\phi$) between the two vectors $\mathbf{e}$ and $\mathbf{r}$ can be calculated as given below.

Where

• $\mathbf{e} \cdot \mathbf{r}$ is the dot product between the normalized vectors $\mathbf{e}$ and $\mathbf{r}$.

• $arccos$ is the angle between the two normalized vectors.

By taking the $arccosine$ of the dot product of the two vectors ($\mathbf{e} \cdot \mathbf{r}$), you can find the angle $\phi$ in radians between the two vectors $\mathbf{e}$ and $\mathbf{r}$ .

How it creates images

• The reflection of light in specular reflection plays an essential role in image formation.

• When the light from an object, such as your face, strikes a smooth mirror, it is reflected in an organized manner.

• The reflected light rays carry the same information as the incident light.

• Thus, it maintains the object's shape, color, and brightness.

• The human eye perceives the reflected light rays and traces their paths back to the mirror.

• It creates an illusion that the light is coming from behind the mirror.

• Thus, the mirror appears to contain an image of the object formed by the coherent reflection of the light rays.

Characteristics of the specular reflection

Given below are some of the main characteristics of specular reflection.

• Smooth surface requirement: Specular reflection requires a smooth surface. If the surface is rough or irregular, the incident light is scattered in various directions, leading to the diffuse reflection.

• Single direction reflection: In specular reflection, all the reflected light rays travel in the same direction, resulting in a focused and coherent reflection.

• Clear image formation: The coherent reflection of light allows for the formation of clear and sharp images of the light source or the other objects.

• Preservation of light: The characteristics of the reflected light, such as its color and intensity, remain the same in specular reflection.

Applications of the specular reflection

The specular reflection offers numerous applications, some of which are mentioned below.

• Mirrors and reflecting telescopes: Mirrors mostly rely on the specular reflection to produce clear images, making in essential in daily life.

• Periscopes an endoscopes: These optical devices are based on the principle of specular reflection. It enables to view the locations that are difficult to see directly.

• Photography and filmmaking: Lighting techniques often take advantage of the specular reflection to create desired visual effects and produce high-quality images.

• Computer graphics: Specular reflection is used in game development to render realistic images, adding realism to the visual scenes.

Conclusion

In conclusion, specular reflection is a fundamental principle in light behavior. It is based on the interaction of the incident light waves with the smooth surface. The law of reflection ensures that the light is reflected orderly, forming clear images on the reflective surfaces. The specular reflection has applications in various technologies that make it an essential concept in the study of optics.

Continue reading

• What is diffuse reflection?

• What is texture mapping?

• What is displacement mapping?

• What is ambient reflection?