## Specular reflection

Specular reflection come from latin word “speculum” which means mirror .Reflection of light where the angle of reflected light equals the angle of incident light ,but on opposite side of the surface normal. It is called regular reflection. So that kinds reflection encountered on smooth surface such as spectacles glasses, mirror , polishes metals or lake water .

Law;- A ray of light coming from the left is incident on the mirror surface . The angle marked “i” is called the angle of incidence, and  it measured from the normal, when ‘i’=45 degree. The incident  ray is reflected by the mirror , the reflected ray of light with an angle of reflection ‘r’, we know

i+r=90 degree   [i=45]

45+r=90

r=90-45

r=45 degree,

so angle of incidence =angle of reflection.

This is law of specular reflection.

Conditions of specular reflections ;

The wavelength of visible light are rather small (will below 1micrometer) ,pure  specular reflection requires a high degree of surface flatness — much more than for microwaves, for example  metal surfaces, fully polished surfaces.

Specular reflection in imaging:-

to diffuse reflection , where the random angular changes are introduced , the image information is preserved upon specular reflection . However, the diffuse reflectors can still be useful as screens in certain imaging instruments; such a screens needs to be placed in an imaging plane.

Image from:- In specular reflection object distance to the reflecting surface is equal  to the image distance to the mirror. So virtual image is formed , this not a real image. When you look at yourself in the mirror, what you see is a virtual image of yourself , and that virtual image is behind the mirror.If a friend of yours looks behind the mirror , there will be no image of you behind the mirror.

Specular reflection in daily life:-

When you are standing outside in daylight and observe  the lake , lake water reflect the outside  world including the sky , trees etc. Because  the water surface  are flat and slightly reflecting. For otherhence  when you standing outside in nightlight and look at a building all windows reflect the inside the building , because artificial illumination inside , and it is dark outside, people from outside can see in, through  the windows panes very well, while from inside at  night , you can’t  see outside, and you only see the reflection of yourself  . If you want to see outside, you must turn the light off inside.

Here the output angle deviate from the angle of incidence, and also depends on the optical wavelength.

*specular reflection has two models

1) Blinn lighting model of specular reflection( open glass reflection)

2) phong  lighting of specular reflection ( natural specular reflection)

Internal reflection :-

We know snell’s law

N /n=sinr/sinR

[N=medium , R= medim angle

n=air, r= angle of air]Phong lighting :  The intensity of reflection is a function of the angle between the viewer and the ideal direction r of reflection of light  from the light source of the surface .

• To compute r note that r+s equals twice the projection of s onton
• The projection of s onto n

(s.n)(n.n)n=(s.n)n

• Therefore ,

r+s=2(s.n)n

r=2(s.n)n-s

computing specular reflection:

•  the specular reflection is proportional to the cosine of the angle between v and r ,

calculated as (r.v)^shiny

Blinn lighting;

• A slightly more efficient method is the blinn lighting method.
• Formula,

r=Lm(h.n)^shiny

[ h= halfway vector, unit vector between s and v, use h.n instead of r.v ]

Specular reflection in ultrasound:   when the sound waves encounter large smooth surface  such as bone , which results in the sound wave being reflect back in a relatively uniform directon.

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Specular reflection in imaging :   specular reflection can be used for imaging for example , in refractive telescopes. In contrast to diffuse reflection , where random angular changes are introduced,the  image information is preserved upon specular reflection .

### Ritika Das

Optometry student Studies at NBMC&H