Variation of Intensity - Modeling and Rendering

According to the phong model the variation of Intensity (I) along with α (since I α cosⁿα) is:

i) for shiny surface (n > 1)

ii) Dull surface  (n ~= 1)

By the Phong specular reflection as:

I or I_spec. = I_s K_s cosⁿα

Here,    I_s → intensity of source

  I OR I_spec → intensity of specular reflected light

 K_s → Specular reflection coefficient effecting intensity in the case while all ambient or diffuse or specular reflection arises as:

I = I_a K_a + I_d K_d cos θ + I_s K_s cosⁿα  

Now, cosⁿ α= (R¯ V¯)ⁿ        (?  Qcosⁿα =  R¯ V¯).

Here,

R¯ → Unit vector in specular reflection direction 

V¯ → Unit vector pointing the viewer

It is | V¯  |  = 1 ;  | R¯ |  = 1.

R¯ V¯=  | R¯ | | V¯ | cos α = 1.1. cos α = cos α.

  ( ⇒ cos α = R¯ V¯)