---
title: "Ambient, diffuse and specular light"
subject: "Computer Graphics"
chapter: 8
key: "semester_5/computer_graphics:ambient-diffuse-specular-expressions"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/ambient-diffuse-specular-expressions
site: BCT Engineering
---

# Ambient, diffuse and specular light

Computer Graphics · Chapter 8: Illumination and Surface Rendering methods

- Asked in: 2073 Shrawan, 7 marks; 2078 Bhadra, 5+5 marks (asked 2 times)
- Video: [5.4 Phong Lighting Model](https://www.youtube.com/watch?v=C6-JLOcsUck) — The CGVR Study Lab
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/ambient-diffuse-specular-expressions
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-8

## Question

Define and explain the terms ambient light, diffuse reflection and specular reflection with appropriate mathematical expressions.

## Short answer

Ambient light: I_amb = ka·Ia, uniform background. Diffuse: I_diff = kd·IL·(N·L), viewer-independent. Specular: I_spec = ks·IL·(R·V)^n, highlight around R. Total Phong: I = ka·Ia + kd·IL·(N·L) + ks·IL·(R·V)^n.

## Answer

#### Ambient light
Ambient light is the uniform background light that comes from reflections off all surrounding objects. It lights every surface equally from all directions and has no direction.

I_amb = ka · Ia

(ka = ambient reflection coefficient, 0 to 1; Ia = intensity of ambient light.)

#### Diffuse reflection
Diffuse reflection is the scattering of light equally in all directions from a rough, dull surface. Its brightness does not depend on the viewing position, but on the angle θ between the surface normal N and the light direction L (Lambert's cosine law).

I_diff = kd · IL · cosθ = kd · IL · (N · L)

(kd = diffuse coefficient, IL = light source intensity.)

#### Specular reflection
Specular reflection is the mirror-like reflection from a shiny surface that gives a highlight. It is strongest in the direction R of ideal reflection and depends on the angle φ between R and the viewing direction V.

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

(ks = specular coefficient, n = shininess exponent, R = 2(N·L)N − L.)

#### Total (Phong) model

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

| Component | Depends on | Appearance |
|---|---|---|
| Ambient | Ia only | Uniform base brightness |
| Diffuse | N and L | Smooth shading, viewer independent |
| Specular | R and V, n | Bright highlight, viewer dependent |

## Check yourself

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

1. What is ambient light?
   A. Uniform background light with no direction, I = ka Ia
   B. Direction-dependent highlight
   C. Light from one point source
   D. Reflected only along R
   Answer: A. It lights all surfaces equally. (Key point: Ambient)

2. Which component depends on the viewer position?
   A. Ambient
   B. Specular
   C. Diffuse
   D. None
   Answer: B. Specular depends on R and V. (Key point: Viewer dependence)

3. Diffuse reflection depends on:
   A. R and V
   B. Ia only
   C. Angle between N and L
   D. n only
   Answer: C. It follows Lambert's cosine law. (Key point: Diffuse inputs)

4. What is the total Phong model?
   A. ka Ia x kd IL x ks IL
   B. kd IL (N.L) only
   C. ks IL (N.L)^n
   D. ka Ia + kd IL (N.L) + ks IL (R.V)^n
   Answer: D. The three components are added. (Key point: Total model)

## Related in Computer Graphics

- [Diffuse reflection equation](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adiffuse-reflection-equation) — Computer Graphics, chapter 8, asked 3×
- [Specular reflection](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aspecular-reflection-expression) — Computer Graphics, chapter 8, asked 4×
- [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
- [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×

## 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
- [Light propagation; define NA and acceptance angle](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Alight-propagation-define-na-acceptance) — Propagation and Antenna, chapter 6