Light and Reflectance

Light and Colour

Most objects don’t emit light—they reflect it. The colour we perceive depends on:

1. Illumination: The light source spectrum
2. Reflectance: How the surface reflects each wavelength

The Reflectance Equation

$L_{\text{reflected}}(\lambda) = I(\lambda) \cdot R(\lambda)$

where:

• $I(\lambda)$ is the illumination spectrum
• $R(\lambda)$ is the surface reflectance function (0 to 1)

Reflectance Properties

Reflectance Function

• Defines what fraction of light is reflected at each wavelength
• Range: $R(\lambda) \in [0, 1]$
• Independent of illumination intensity

Examples

Surface	Reflectance Characteristic
White paper	High reflectance across all wavelengths
Red surface	High reflectance in long wavelengths, low elsewhere
Blue surface	High reflectance in short wavelengths
Black surface	Low reflectance across all wavelengths

Why Colours Change Under Different Lighting

The same object can appear different under different illumination:

• White object under red light: Appears red (reflects only red)
• Blue object under sodium street lights: Appears dark grey (sodium light has no blue component to reflect)

Metameric Shift

Two surfaces that match under one light source may not match under another. This is called metameric shift.

Illuminant Types

Standard Illuminants

Illuminant	Description	Colour Temperature
D65	Average daylight	6500 K
D50	Horizon daylight	5000 K
A	Incandescent tungsten	2856 K
F2	Cool white fluorescent	4230 K

Reflectance and Material Perception

Diffuse Reflection

Light scattered equally in all directions (matte surfaces):

$L_{\text{diffuse}} = k_d \cdot I \cdot \max(0, \mathbf{n} \cdot \mathbf{l})$

Specular Reflection

Mirror-like reflection dependent on viewing angle:

$L_{\text{specular}} = k_s \cdot I \cdot \max(0, \mathbf{r} \cdot \mathbf{v})^n$

Practical Implications

Colour Consistency

• Colour management systems must account for illuminant
• Print proofs use standardised lighting (D50)
• Displays assume D65 white point

Material Appearance

• Gloss vs matte: Specular vs diffuse reflection ratio
• Texture: Micro-geometry affects reflectance distribution
• Subsurface scattering: Light enters and exits at different points

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Summary

• Perceived colour = illumination × reflectance
• Reflectance function defines surface colour independent of light source
• Colours can change under different illumination
• Different materials have different reflection characteristics

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Past Paper Questions

2024 Paper 3 Question 3: Explain why a blue object appears dark under sodium street lights.

2023 Paper 3 Question 3: What is the reflectance function? How does it relate to perceived colour?

2022 Paper 3 Question 3: A red surface viewed under green light appears dark. Explain why.