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Calculations and theLaws of Illumination

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Terms

Luminous Intensity (I)

Luminous flux (F)

Illuminance (E) Luminance (L)

Candela (cd)

Lumen (lm)

Lux (lx) Nit (nt)

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Terms

Luminous Intensity (I)

The illuminating power of a light source

Luminous flux (F) The flow of light measured in lumens

Illuminance (E)

The measure of light falling on a surface

Luminance (L)

The measured brightness of a surface

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The laws

There are 2 important laws in illumination,

these are:

Inverse Square Law Cosine Law

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Inverse Square Law

This law assumes thatthe illuminationreceived on a surface

from a light source isinversely proportional tothe square of itsdistance from thesource

In other words, thefurther away, the lessillumination

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Inverse Square Law

The inverse square law

can be calculated by:

Where E is illuminance I is Luminous intensity

d is distance

luxd

IE2

!

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Example

The illuminance on a surface directly below a

point source is 400 lux. If the distance

between the light source and the surface is2m, what is the intensity of the light source?

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Solution

The solution assumes

that the lamp is a

filament or energy

saver type

A long fluorescent type

does not use this law

luxd

IE

2!

2dEI v!

4400v!I

cdI 1600!

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Example 2

A standard incandescent lamp having a

luminous intensity of 100 cd in all directions

gives an illuminance of 40 lux at the surfaceof a bench vertically below the lamp.

What distance is the lamp above the bench?

What iilluminance would be received at the

bench?

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2

d

I!

E

Id !

40

100

!d

md 58.1!

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d = 1.58-0.58

d = 1m

2

d

IE!

1

100!E

luxE 100!

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Now try the questions

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Cosine Law

This method allows us

to calculate the

illuminance with one or

more lamps or withreflection from

surroundings.

Ucos2v!

d

IE

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Problem with Cosine Law

With the Cosine Law, d

is difficult to measure

so we use Pythagoras

to determine the height.

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Problem with Cosine Law

Since

and

Equation becomes:

d

h!cos

Ucos

dh !

U

U

cos

)cos

( 2v!

h

IE 3

2cosUv!

h

IE

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Example

An incandescent lamp

is suspended 3m above

a level workbench and

is fitted with a reflectorso that the luminous

intensity is 400cd.

Calculate the

illuminance at point aand also at point b

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Example

Point a

In this case d = h

2d

IE!

2h

IE!

lxE 4.449

400!!

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Example

Point b

In this case d = h

= 9.6lx

Ucos2v!

d

IE

6.02v!

d

IE

6.025400 !!E