Specular And Diffuse Reflection: 13 Important Concepts


What is specular reflection of light? | What is regular reflection ?

Specular reflection definition :

Specular reflection refers to the phenomenon of reflection of parallel light rays falling on a surface, at equal angles. Specular reflection is carried out by smooth surfaces such as mirrors. The Specular reflection follows all the 3- laws of reflection i.e. the angle of reflection is equal to the angle of incidence, the normal, incident, and reflected ray all lie on the same plane. The incident ray and the reflected ray are on other sides of the normal.

What is diffuse reflection? | What is meant by diffuse reflection ?

Diffuse reflection definition | non specular reflection :

Diffuse reflection refers to the phenomenon of reflection of parallel light rays falling on a surface, at different angles. Diffused reflection is carried out by rough surfaces such as roads, walls, etc. 

Note : For a diffused reflection to be ideal, it has to follow and demonstrate the Lambertian laws of reflection. According to this, the luminance is the same for all directions present in the half-space that is adjoining to the reflecting surface. Diffused reflections are sometimes termed non-specular reflections.

Does diffused reflection mean the failure of the laws of reflection ? | Does diffuse reflection follow the law of reflection ?

Diffused reflection like specular reflection follows all the laws of reflection. The angle of reflection is equalized to the angle of incidence where both the angles are measured from the normal, and normal, incident ray, and reflected ray at the point of incidence are in the same plane. The incident ray and the reflected ray are present on opposite sides of the normal.

Diffuse reflection examples

Diffuse reflection. Image source: Jeff DahlDiffuse reflectionCC BY-SA 3.0

What are the components of reflection ?

What are the Laws of reflection?

Laws of reflection | law of specular reflection

The laws of reflection are given as:

  • The angle of reflection is equal to the angle of incidence where both the angles are computed from the normal planes.
  • The normal, incident, and reflected rays at the point of incidence all stay in the same identical plane.
  • The incident ray and the reflected ray are existed in other/opposite sides to the normal.

Image credit : Nilock, Public domain, via Wikimedia Commons



a line at 90° to the surface of a reflected medium.

Incident ray:

A ray of light going to the reflected medium.

Reflected ray:

A ray that comes off the reflected medium.

Angle of incidence:

The angle between the incident ray and the normal.

Angle of reflection:

The angle between the reflected ray and the normal.

What is the difference between specular and diffuse reflection? | How does specular reflection differ from diffuse reflection ?

Specular reflection vs Diffused reflection

Specular reflectionDiffused reflection
Reflection of incident parallel light rays occurs at equal angles.Reflection of incident parallel light rays occurs at unequal angles.
Requires the reflecting surface to be very smooth.Requires the reflecting surface to be rough.
Follows all the laws of reflection to form an image.Follows the laws of reflection to scatter light.
Example: reflection by a mirror / polished metal surface.Example: reflection by aby unpolished/rough surface like roads, walls, etc.
Reflectance is zero for all angles except the exact reflected angle.There is some non-zero reflectance value present for approximately every angle.
Specular and diffuse reflection
Specular and diffuse reflection. Image source; GianniG46Lambert2CC BY-SA 3.0

What is reflectance?

Reflectance definition

The surface reflectance of a material is defined as the efficiency of the material to reflect the incident radiant energy. In other words, reflectance refers to the ratio of the power of the reflected light ray to the incident light ray from the plane of the material.

Diffuse reflectance measurement

The specular reflectance that is valid for smooth glass or polished metal surfaces approximately comes out to be zero for all angles except at the applicable reflected angle. This angle is the reflected-angle that has a value equivalent to the angle of incidence on the opposite side of the normal, and in case the incident ray falls normally on the surface of the material then it is reflected back to the same direction i.e. both the reflected angle and the incident angle is equal to 0o.

The diffuse reflectance for certain materials like matte white paint comes out to be uniform i.e. the luminous flux gets equally or near-equally reflected at all angles. Such materials are said to follow the Lambertian laws of reflection. In the practical world, materials demonstrate a mix of diffuse and specular reflective properties.

What is Diffuse reflectance spectroscopy ?

Diffuse reflectance spectroscopy principle

Diffuse reflectance spectroscopy refers to a highly developed method or technique of observing and analyzing the spectral characteristics of opaque solid objects. The method of diffuse reflectance spectroscopy works by taking into consideration the phenomenon of internal reflection of light which is diffuse along with the external surface reflection of light which is specular.

The technique of diffuse reflectance spectroscopy is considered to be extremely useful for analyzing and observing the interactions between several formulation components. This method has been successfully used for characterizing numerous solid-state reactions. In one such experiment, the Investigation used this method with suitably designed stress conditions for examining and carrying different types of specialized-excipient interactions, degradation pathways, and altering the bioavailability based on the chemisorption of the sample material to some different components during the formulation.

Diffuse reflective photoelectric sensor

In a diffuse reflective photoelectric sensor, the Source of light and the light receiver are present in the same instrument. Diffuse reflective photoelectric sensors are capable of sensing things when the beam of light that is emitted towards the given target suffers reflection on the target surface and gets directed back to the detector.

These types of diffused sensors are widely used for automation applications because they are handier or more compact (because most of the sensing components are present in the single cover) than most other sensors that serve the same function.

Diffused reflective photoelectric sensors are mainly used for:

  • Detecting a number of objects from a common conveyor unit.
  • Detecting translucent materials.
  • Detecting the level of substance present inside different containers.
  • To Detect the existence of part, box, and web material.
  • Detecting certain identifying features for determining the orientation of an object.
  • Detecting error conditions for object examination works.

Diffused reflective photoelectric sensors are user-friendly because they are fuss-free in terms of installation procedure because all the components are included in a single unit and are also pocket-friendly sensing solutions. However, like any other device, diffused reflective photoelectric sensors also have certain drawbacks.

These sensors provide less accurate results when it is used for sensing position than thru-beam detection. These sensors are also found to be less effective on translucent objects. Moreover, it is seen that such types of sensors get easily affected by surface color, the texture of the material, the angle of incidence, physical target characteristics, and inhomogeneous environments.

Diffuse reflectance spectroscopy instrument

Diffuse reflectance spectroscopy instruments provide measurements by aligning the material in front of the incident light window, and then a concentrated light beam is reflected from the object to the detector with the help of a sphere coated by barium sulfate internally. The value obtained from this set-up is the reflectance or relative reflectance of the material in question with respect to the standard reference reflectance of a whiteboard that is considered to be equal to 100%.

The light is then directed towards the given material at an angle of 0°. During this, the specularly reflected light leaves the integrating sphere and is therefore not sensed by the detector. Due to this reason, this set-up is capable of measuring only the diffuse reflected light. However, new models of integrating spheres are designed that are capable of sending light beams at different incidence angles. These models can therefore calculate the combination of both specular and diffuse reflected light.

What happens during specular reflection ?

Specular reflection slit lamp

The phenomenon of specular reflection is applied for visualizing and analyzing the functionality of the corneal and lens surfaces of the human eye. It is clear to us that when the reflecting surface is smooth, the reflection will be regular or specular and when the reflecting surface is uneven or rough, the reflection will be irregular or diffused. This is used for examining the normal exterior of the corneal endothelium. This method is carried out by positioning the illuminator at around 30 degrees on one side and the microscope at 30 degrees to the opposite side. The angle of the microscope to the illuminator has to be equal and opposite.

For visualizing the endothelium, one has to start with a lower magnification ranging from about 10X to 16X. A comparatively narrow beam of light has to be directed onto the cornea in such a way that the reflection of light from the corneal epithelium glares your eyes. After that, one needs to slightly move the narrow beam of light to the side, and look next to it, at the reflection coming from the endothelial surface.

After this one has to shift to the highest possible magnification. The height of the slit beam can be lightly lowered for reducing the glare. When we widen the slit, we enhance the field of view but reduce the contrast. It is found that the corneal endothelium can be best observed while using only a single ocular lens. Hence, one might close the non-viewing eye for better results.

The method described here requires a lot of test for proper evaluation. This is because the corneal endothelial cells have a very faint contrast, and requires some experience detecting properly. The Cells that are counted only by the slit lamp technique are not usually accepted. The results found by contact specular microscopy are considered to provide much more precise results.

What is FTIR ?

Specular reflectance FTIR

In FTIR (Fourier transform infrared), Specular reflectance sampling is considered a very crucial method that is used for measuring the thin films on reflective substrates, analyzing the bulk samples and measuring the mono-molecular layers on the material of a substrate. This method is widely popular because it allows observation and analysis of samples without the requirement of any sample preparation. This also helps in keeping the sample material not impacted for all the succeeding measurements.

The first part of the sampling method is to measure the reflected luminous flux from the surface of the material at a given angle of incidence. At the end of the surface of the material, the occurrence of certain electromagnetic and physical phenomena is observed and is reliant on the angle of incidence of the illuminating beam, index of refraction of the material, and thickness of the material and other samples and then prevalent experimental conditions.

What is the formula of specular reflection ?

Specular reflection formula

The law of reflection can be demonstrated by using the properties of linear algebra. The direction of a reflected vector can be calculated by the direction of the incident vector and the surface normal vector.

In a given incident direction di from the source of light to the surface of the material and let the surface normal direction dn, the specularly reflected direction ds is given by the equation:

[Latex]\hat{d_{s}}= 2(\hat{d_{n}}.\hat{d_{i}})\hat{d_{n}}-\hat{d_{i}}[/Latex]

where dn. di is a scalar quantity that is generated by the dot product of the two vectors.

In this equation, certain authors may describe the incident and reflection directions with different signs convention.

If we assume the representation of these Euclidean vectors in column form, then the given equation can be equally conveyed as a matrix-vector multiplication:

[Latex]\hat{d_{s}}= R\hat{d_{i}}[/Latex]

Where R refers to the Householder transformation matrix and is defined as:

[Latex]R= I-2\hat{d_{n}}\hat{d_{n}}^{^{T}}[/Latex]

R is given ten terms of an identity matrix I and two times of the outer product of dn.

Specular reflection coefficient

Let us consider a light beam coming from a distant point source of light in the direction given as ~s. This light beam gets reflected back into a range of directions around the perfect mirror directions ~m = 2(~n · ~s) ~n −~s.

One such common representation of this is given by the following expression:

 Ls ( ~de) = rsI max(0, ~m · ~de) α  

Here, the term rs is referred to as the specular reflection coefficient (that frequently assumes a value equal to 1 − rd), ‘I’ refers to the power of the incident power from the given point source, and α≥0 is taken as a constant, known as width of the specular highlight.

With the increase in the value of α, there is a decrease in the effective width of the specular reflection, This arrangement becomes a mirror when the limit as α increases.

What is specular reflection used for ?

Applications of Specular and Diffuse Reflection

A number of applications of diffuse reflection and specular reflection can be found in our day-to-day lives. Here, we are going to discuss two major applications that we experience almost every day:

  1. Diffused reflection: When we drive an automobile, any form of glare makes concentrating on the road difficult for the driver. In the rainy seasons, when a major part of the road is wet and reflects the light coming from the headlights of other cars, it becomes difficult to drive. This glare will result of the specular reflection of the beam of the light, However, the rough surface of the roads helps in maintaining a diffused reflection that reduces the glare on the driver’s eyes. When water fills up the cervices of the road, it becomes smoother leading to specular reflection.
  2. Specular reflection: Now, let us consider an application of reflection in photography. All of us have seen and applauded beautiful sceneries of nature comprising of a calm water body in the foreground reflecting the objects present in the background, sideways, or overhead. When the water is calm, its surface is smooth and it acts like a mirror applying the principle of specular reflection for forming images. Now, for the camera, the camera lens might directly receive the reflected light rays from the water body (undergoing specular reflection). If the light hit another rough surface (undergoing diffused reflection) before reaching the camera, then the camera lens would not be able to capture the image of water body reflection. Therefore, only when specular reflection sends a wide beam of light together to the lens of the camera and it is able to form an exact replica image.

Numerical on Specular and Diffused reflection

Consider three parallel rays of light. These light rays are then made to be incident on a rough bumpy surface at marginally different angles, as shown in the figure below. The incident angles for the rays are given as 15o for ray A (blue in figure), 31o for ray B (green), and 47o for ray C (red). 

(a)  What will be the angles of reflection for each of the three rays? 

(b) Is it possible that the three rays remain parallel after undergoing reflection? 

(c)  Draw the path of the reflected light rays.


(a)We know from the laws of reflection’s statement that the angle of reflection is equivalent to the angle of incidence for each ray, and therefore, the angle of incidence for ray A will be 15o, angle of incidence for ray B will be  31o, and angle of incidence for ray C will be  47o.
(b)No, as the surface is mentioned to be rough and bumpy, the three rays will diffuse after reflection and will not be parallel to each other.
(c)The figure drawn below shows the path of each light ray after undergoing reflection from the given surface.

Which reflects more light tissue paper or glass window ?

Tissue paper if not black will reflect more light than glass. In addition glass is transparent , permit light to pass thru.

Why cant you see your reflection in all objects that reflect light ?

The main reason we may not see reflection from all the object is because the light reflected by those objects might be scattered.

To know about thin film interference click here

Sanchari Chakraborty

I am an eager learner, currently invested in the field of Applied Optics and Photonics. I am also an active member of SPIE (International society for optics and photonics) and OSI(Optical Society of India). My articles are aimed towards bringing quality science research topics to light in a simple yet informative way. Science has been evolving since time immemorial. So, I try my bit to tap into the evolution and present it to the readers. Let's connect through https://www.linkedin.com/in/sanchari-chakraborty-7b33b416a/

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