---
title: "Define terms; Phong intensity equation"
subject: "Computer Graphics"
chapter: 8
key: "semester_5/computer_graphics:define-terms-lambert-phong-equation"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/define-terms-lambert-phong-equation
site: BCT Engineering
---

# Define terms; Phong intensity equation

Computer Graphics · Chapter 8: Illumination and Surface Rendering methods

- Asked in: 2071 Chaitra, 10 marks
- Video: [Illumination Model: Ambient Illumination| Diffused Reflection| Specular Reflection in just 15 min!](https://www.youtube.com/watch?v=hS1VowQ2es0) — Vinay Mishra
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/define-terms-lambert-phong-equation
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-8

## Question

Define the terms: i) Ambient light ii) Lambert cosine law iii) Diffuse reflection iv) Specular reflection. Also find equation for intensity of point by using Phong illumination model.

## Short answer

i) Ambient: uniform background light, I=ka·Ia. ii) Lambert’s law: diffuse reflected intensity ∝ cosθ = N·L. iii) Diffuse: scattering equally in all directions, brightness independent of view. iv) Specular: mirror-like highlight, I=ks·IL·(Ř·V)^n. Phong equation: I = ka·Ia + kd·IL·(Ř·L) + ks·IL·(Ř·V)^n.

## Answer

#### i) Ambient light
Ambient light is the uniform background light from reflections off many surrounding surfaces. It has no direction and lights every surface equally. Contribution: I_amb = ka · Ia.

#### ii) Lambert's cosine law
The intensity of diffusely reflected light from a surface is proportional to the cosine of the angle θ between the unit surface normal N and the unit vector L to the light source:

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

A surface turned away from the light receives (and reflects) less light.

#### iii) Diffuse reflection
Diffuse reflection is the scattering of incident light equally in all directions by a rough, dull surface. The brightness does not depend on the viewing position but only on the light direction and the normal (Lambert's law).

#### iv) Specular reflection
Specular reflection is the mirror-like reflection from a shiny surface, concentrated around the direction of ideal reflection R, producing a highlight that moves with the viewer. Phong model: I_spec = ks · IL · (R · V)^n.

#### Phong illumination equation
Summing the three components for a point light source:

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

with
- R = 2(N·L)N − L (reflection vector), V = unit vector to the viewer
- ka, kd, ks = ambient, diffuse, specular coefficients; n = shininess exponent

With distance attenuation and m lights:

I = ka·Ia + Σ f(d_l)·IL_l·[ kd (N·L_l) + ks (R_l·V)^n ], f(d) = min(1/(a0 + a1d + a2d²), 1)

Terms are set to 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. According to Lambert's cosine law, diffuse intensity is proportional to what?
   A. The cosine of the angle between R and V
   B. The viewing distance
   C. The sine of the angle between N and L
   D. The cosine of the angle between N and L
   Answer: D. I_diff = kd*IL*cos(theta) = kd*IL*(N.L). (Key point: Lambert's law)

2. What characterises diffuse reflection?
   A. Light scatters equally in all directions from a rough surface, so brightness is independent of viewer position
   B. Light concentrates around R and the highlight moves with the viewer
   C. Light is uniform with no direction from all surroundings
   D. Light passes through the surface
   Answer: A. Diffuse brightness depends only on N and L, not on the viewing position. (Key point: Diffuse reflection)

3. Which term gives the specular highlight in the Phong model?
   A. ka*Ia
   B. ks*IL*(R.V)^n
   C. kd*IL*(N.L)
   D. ks*IL*(N.L)^n
   Answer: B. Specular light is concentrated near the reflection direction R; the exponent n controls how sharp it is. (Key point: Specular reflection)

4. What is true of ambient light?
   A. It depends on the angle between N and L
   B. It depends on the angle between R and V
   C. It is uniform, directionless background light that lights all surfaces equally, contributing ka*Ia
   D. It is produced only by a spotlight
   Answer: C. Ambient light has no direction, so its term is the constant ka*Ia. (Key point: Ambient light)

5. How is the reflection vector R computed in the Phong equation?
   A. R = L - 2(N.L)N
   B. R = N + L
   C. R = (N.L)L - N
   D. R = 2(N.L)N - L
   Answer: D. R is L mirrored about the normal N: R = 2(N.L)N - L. (Key point: Reflection vector)

## Related in Computer Graphics

- [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×
- [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×
- [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×

## 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