Illumination of a surface: E=(I cosθ)/(d^2) The illumination E of a surface by a light source is

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Illumination of a surface: E=(I cosθ)/(d^2) The illumination...

Illumination of a surface: $E=\frac{I \cos \theta}{d^{2}}$ The illumination $E$ of a surface by a light source is a measure of the luminous flux per unit area that reaches the surface. The value of $E$ [in lumens (Im) per square foot $\rfloor$ is given by the formula shown, where $d$ is the distance from the light source (in feet), $I$ is the intensity of the light [in candelas (cd)], and $\theta$ is the angle the light source makes with the vertical. For reading a book, an illumination $E$ of at least $18 \mathrm{lm} / \mathrm{ft}^{2}$ is recommended. Assuming the open book is lying on a horizontal surface, how far away should a light source be placed if it has an intensity of $90 \mathrm{cd}$ (about $75 \mathrm{W}$ ) and the light flux makes an angle of $\left.65^{\circ} \text { with the book's surface (i.e., } \theta=25^{\circ}\right) ?$ GRAPH CANT COPY

Illumination of a surface: $E=\frac{I \cos \theta}{d^{2}}$
The illumination $E$ of a surface by a light source is a measure of the luminous flux per unit area that reaches the surface. The value of $E$ [in lumens (Im) per square foot $\rfloor$ is given by the formula shown, where $d$ is the distance from the light source (in feet), $I$ is the intensity of the light [in candelas (cd)], and $\theta$ is the angle the light source makes with the vertical. For reading a book, an illumination $E$ of at least $18 \mathrm{lm} / \mathrm{ft}^{2}$ is recommended. Assuming the open book is lying on a horizontal surface, how far away should a light source be placed if it has an intensity of $90 \mathrm{cd}$ (about $75 \mathrm{W}$ ) and the light flux makes an angle of
$\left.65^{\circ} \text { with the book's surface (i.e., } \theta=25^{\circ}\right) ?$
GRAPH CANT COPY

Key Concepts

Luminous Intensity

Luminous intensity is the measure of the wavelength-weighted power emitted by a light source in a particular direction, quantified in candelas. It forms the basis for calculating how a light source distributes its output over space, which directly affects the illuminance on surfaces at varying distances.

Inverse Square Law

The inverse square law is a key principle stating that the illumination (or intensity) from a point source decreases in proportion to the square of the distance from the source. This law is central in lighting calculations, as it describes how the distribution of light energy dilutes over an expanding area with increasing distance.

Illuminance

Illuminance represents the amount of luminous flux per unit area incident on a surface. It is a fundamental concept in photometry that quantifies how well a surface is lit, with common units including lux and lumens per square foot. This measure is crucial for designing lighting systems and ensuring adequate light levels for various tasks.

Angle of Incidence Correction

The angle of incidence correction accounts for the fact that the effective illumination on a surface varies with the cosine of the angle between the incoming light and the surface normal. By including a cosine factor in the illumination formula, the calculation adjusts for reduced effectiveness when light strikes the surface obliquely, ensuring an accurate estimation of the illuminance.

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