---
title: "Specular reflection"
subject: "Computer Graphics"
chapter: 8
key: "semester_5/computer_graphics:specular-reflection-expression"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/specular-reflection-expression
site: BCT Engineering
---

# Specular reflection

Computer Graphics · Chapter 8: Illumination and Surface Rendering methods

- Asked in: 2082 Kartik (new course), 1 marks; 2068 Chaitra, 4 marks; 2069 Chaitra, 7 marks; 2075 Chaitra, 8 marks (asked 4 times)
- Video: [Specular Reflection | CG | Computer Graphics | Lec-50 | Bhanu Priya](https://www.youtube.com/watch?v=xJMxkXVrwyg) — Education 4u
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/specular-reflection-expression
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-8

## Question

Define specular reflection and explain the Phong model for specular reflection, with the intensity expression (for a point light source).

## Short answer

Specular reflection is the mirror-like highlight from a shiny surface. The Phong model gives I_spec = ks·IL·(R·V)^n, where R = 2(N·L)N−L, n is the shininess exponent. Total intensity: I = ka·Ia + IL[kd(N·L) + ks(R·V)^n].

## Answer

**Specular reflection** is the mirror-like reflection of light from a shiny surface, producing a bright spot (highlight) on the surface. The reflected light is concentrated around the direction of ideal reflection R, so the highlight is seen only when the viewer is near that direction. For a perfect mirror, light is reflected only in the direction R; for real surfaces it spreads in a narrow cone.

**Phong specular model.** The intensity of the specular reflection is proportional to cos^n φ, where φ is the angle between the direction of reflection R and the viewing direction V.

I_spec = ks · IL · cos^n φ = ks · IL · (R · V)^n

- ks = specular reflection coefficient (0 to 1, may depend on the incidence angle)
- IL = intensity of the point light source
- n = specular reflection exponent (shininess): 1 for very rough surfaces, 100 or more for very shiny metals; larger n gives a smaller, sharper highlight
- L = unit vector to the light, N = unit surface normal, V = unit vector to the viewer
- R = reflection vector = 2(N·L)N − L

```text
  N   R
  | /   . 
  |/ phi V
--+---------- surface
   \ L
```

The Blinn-Phong version uses the halfway vector H = (L + V)/|L + V| and (N·H)^n, which avoids computing R.

Total with ambient and diffuse:

I = ka·Ia + IL [ kd (N·L) + ks (R·V)^n ]

(Specular is taken as zero when N·L < 0 or R·V < 0.)

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is specular reflection?
   A. Mirror-like reflection giving a highlight near direction R
   B. Even scattering in all directions
   C. Uniform background light
   D. Light absorbed by surface
   Answer: A. It is concentrated around the ideal reflection direction. (Key point: Definition)

2. What is the Phong specular intensity?
   A. kd . IL . (N . L)
   B. ks . IL . (R . V)^n
   C. ka . Ia
   D. ks . IL . (N . L)
   Answer: B. cos^n of the angle between R and V. (Key point: Phong expression)

3. How is R computed?
   A. R = N + L
   B. R = L - 2N
   C. R = 2(N . L)N - L
   D. R = (L + V)/|L + V|
   Answer: C. This reflects L about the normal. (Key point: Reflection vector)

4. Larger n gives:
   A. A larger, softer highlight
   B. No highlight
   C. Brighter ambient
   D. A smaller, sharper highlight
   Answer: D. The cosine power falls off faster. (Key point: Effect of n)

## Related in Computer Graphics

- [Phong illumination model expression](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aphong-illumination-model-derive) — Computer Graphics, chapter 8, asked 8×
- [Define terms; Phong intensity equation](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adefine-terms-lambert-phong-equation) — Computer Graphics, chapter 8
- [Ambient, diffuse and specular light](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aambient-diffuse-specular-expressions) — Computer Graphics, chapter 8, asked 2×
- [Distance consideration in intensity](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aintensity-attenuation-distance) — Computer Graphics, chapter 8, asked 2×
- [Gouraud intensity at midpoint P](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Agouraud-intensity-midpoint-scan-line) — Computer Graphics, chapter 8
- [Intensity at centroid of a triangle](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Atotal-intensity-triangle-centroid) — Computer Graphics, chapter 8

## Related in other subjects

- [Light sources and specular reflection principle](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Alight-sources-specular-reflection) — Industrial Power Distribution and Illumination, chapter 6
- [Total internal reflection as light conduit](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Atotal-internal-reflection-light-conduit) — Propagation and Antenna, chapter 6
- [Scattering and two-ray ground reflection model](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Ascattering-two-ray-ground-reflection) — Wireless Communication, chapter 3
- [Source current expression and time to reach 25 mA](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Asource-current-25ma-time-classical) — Electrical Circuit Theory, chapter 3