Environmental physics II
Arch 452
Lecture # 3
Dr Hussain Alzoubi
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E1=
2
E2=(900/18)*sin 45
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Inclined surfaces and cosine law
Case 1
Light source
I cos 
d
I

I sin
A
Inclined
surface
90-


E (at A) = (I
cos/d2
Special case: if  = 0, then
E (at A) = (I/d2
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Inclined surfaces and cosine law
Case 2:

d
I

I sin 

Inclined
surface
90-
I cos 
A


cos  cos  + I sin  sin)/d2
E (at A) = (I
Special case: if  = 0 and  = 0 then
E (at A) = (I
cos  cos  + I sin  sin)/d2
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1
0
E (at A) = I
/d2
if  = ,
then E
(at A) = I
/d2
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Inclined surfaces and cosine law
Case 3: alternative solution

Inclined
surface
d
I

I sin (- )
I cos (- )
A
90-


E (at A) = I
cos ( - ) /d2
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Example:
A building has a roof tilted 30 from the horizon receives
light with luminous intensity I = 1000 Cd. The distance
between the source and point A is 10 feet and the angle
between the light rays and the vertical axis is 45. (see figure
1). Find the illuminance value at point A in Lux.
45
d= 10 ft
I=1000
A
Inclined
surface
30
Figure 1
Solution : (alternative 1)
E (at A) = (I cos  cos  + I sin  sin)/d2
E (at A) = (1000 x cos 45 cos 30 + 1000 x sin 45 sin 30)/(10)2
E (at A) = (612.37 + 353.55)/100
E (at A) = 9.66 Fc.
E (at A) = 9.66 x 10.76 Lux.
E (at A) = 103.9 Lux
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Solution : (alternative 2)
E (at A) = I cos ( -)/d2
E (at A) = 1000 x cos (45-30 )/(10)2
E (at A) = (1000 x cos 15) /100
E (at A) = 9.66 Fc.
E (at A) = 9.66 x 10.76 Lux.
E (at A) = 103.9 Lux
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Definitions:
Luminous Flux: is the rate at which light is emitted by a light source
( unit is Lumen, lm), symbol is Phi ()
Illuminance : The density of luminous flux on a surface, is measured in foot-candles
(one lumen per square foot) or lux (one lumen per square meter) symbol is E.
Luminous intensity: is the measure of the intensity of light emitted in a given
direction , symbol is (I), unit of measurement is Candela (cd) .
I = Phi (Flux)/W(solid angle(steredian).
Luminance : it is the measure of the perceived brightness of a light source
or illuminated surface, symbol (L) , unit of measurement is Foot lambert
(Candela/ft2 ) or Nit (Candela/m2).
Reflectance: Symbol : ( R); R= Total reflected light/Total incident light.
Transmittance : symbol : (T); T= total transmitted light /total incident light.
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Efficacy: number of lumen per watt, the quotient of the total luminous flux
emitted by the total lamp power input. It is expressed in lumens per watt (lm/W).
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brightness
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