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â&#x2C6;&#x201A; r OP â&#x20AC;¢ â&#x2C6;&#x201A; r OP =  & & & & = [sin(θ ) cos(Ï&#x2020; ) x0 + sin(θ ) sin(Ï&#x2020; ) y 0 + cos(θ ) z 0 ] â&#x20AC;¢ [sin(θ ) cos(Ï&#x2020; ) x0 + & & sin(θ ) sin(Ï&#x2020; ) y 0 + cos(θ ) z 0 ] = = sin(θ ) 2 cos(Ï&#x2020; ) 2 + sin(θ ) 2 sin(Ï&#x2020; ) 2 + cos(θ ) 2 = sin(θ ) 2 [cos(Ï&#x2020; ) 2 + sin(Ï&#x2020; ) 2 ] + cos(θ ) 2 = = sin(θ ) 2 + cos(θ ) 2 = 1   3HUWDQWRVLSXzFRQFOXGHUH

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= [ r cos(θ ) sin(θ ) cos(Ï&#x2020; ) 2 + r cos(θ ) sin(θ ) sin(Ï&#x2020; ) 2 â&#x2C6;&#x2019; r sin(θ ) cos(θ ) =  = r cos(θ ) sin(θ )[cos(Ï&#x2020; ) 2 + sin(Ï&#x2020; ) 2 ] â&#x2C6;&#x2019; r sin(θ ) cos(θ ) = r cos(θ ) sin(θ ) â&#x2C6;&#x2019; r sin(θ ) cos(θ ) = 0 

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= v x r cos(θ ) cos(φ ) + v y r cos(θ ) sin(φ ) − v z r sin(θ )  vθ = v x r cos(θ ) cos(φ ) + v y r cos(θ ) sin(φ ) − v z r sin(θ )  & & & & & & & V • ∂ φ OP = vθ = (v x x0 + v y y 0 + v z z 0 ) • [−r sin(θ ) sin(φ ) x0 + r sin(θ ) cos(φ ) y 0 − 0 z 0 ] =  = −v x r sin(θ ) sin(φ ) + v y r sin(θ ) cos(φ )  




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+∞

−∞

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=

φ + Δφ θ + Δθ dS =³ dφ ³ sin(θ ) dθ = Δφ [cos(θ ) − cos(θ + Δθ )]   2 φ θ r

dS ′ dS = cos(ψ ) 2   2 r r

­1 °σ ° °1   ® °σ °1 ° ¯σ

dx 1 = v x ( x, y , z ) dt ρ dy 1 = v y ( x, y, z )   dt ρ dz 1 = v z ( x, y , z ) dt ρ & &   Ψ = ³³ V • n dS   S

&

dΨ   cos(ψ )dS &   dΨ = (∂ x v x + ∂ y v y + ∂ z v z ) dzdxdy = ∇ • Vdτ   & & &   Ψ = ³³ V • n dS = ³³³ ∇ • Vdτ     V

=

τ

S

  Ψ

=

Ω2

&

& &

³ V (Ω) dΩ = ³³V • n sin(θ )dθdφ  

Ω1

&

S

  V ( Ω ) =

dΨ   dΩ n

  QTOT

= ¦ ni q i   i =1




(OHPHQWLGL)RWRPHWULD,QGLFHGHOOHHTXD]LRQL

  Ψ

& & = ³³ V • n dS = ³³ (v x n x + v y n y + v z n z ) dxdy   S

S

& & 2 2 2   Ψ = ³³ V • n dS = ³³ v r n r + r [vθ nθ + sin(θ ) vφ nφ ] r dθ dφ  

{

S

S

S

S

}

& & 2   Ψ = ³³ V • n dS = ³³ ( wr n r + wθ nθ + wφ nφ ) r dθ dφ   Ω2 & & & & & = ³³ V • n dS = ³³ V cos(ψ )dS = ³³ V dS ′ = ³ V r 2 dΩ  

  Ψ

S

S

Ω1

S

 

& & ∂ & & E • t ds = − B • ndS   ³l ∂t ³³S

 

³ H • t ds = ³³

& &

S

l

& & & & ∂ j • ndS + ³³ D • ndS   ∂t S

& & ∂B     ∇ × E = − ∂t & & & ∂D     ∇ × H = j + ∂t & ∂2 &   ∇ E = εμ 2 E   ∂t 2

­ 2 ρ ∂2 εμ ∇ Π = Π=− ° 2 ε0 ∂t °   ® &   2 °∇ 2 A& = εμ ∂ A& = − j °¯ ε0 ∂t 2 & & & &   E = E x [Φ ( x, y , z , t )] x 0 + E y [Φ ( x, y , z , t )] y 0 + E z [Φ ( x, y , z , t )] z 0     ∂

2

j

E i = ∂ 2 Φ E i ⋅ (∂ j Φ ) = ∂ 2 Φ E i ⋅ (k j )   2

2

ª 3 (k h )2 º» ¦ « 3 & ª 2º 2 i 2 » ∂ 2 4 E i ei     ∇ E = «¦ (k h ) » ∂ Φ E ei = « h =1 2 « ω » ¬ h =1 ¼ «¬ »¼ ª 3 2 º « ¦ (k h ) » » = v 2 = εμ     « h =1 2 « ω » «¬ »¼ & & ' & ' & ' & & &   E = E x [ K • r − ωt )]x 0 + E y [ K • r − ωt ] y 0 + E z [ K • r − ωt ] z 0  




(OHPHQWLGL)RWRPHWULD,QGLFHGHOOHHTXD]LRQL

&

& & & = E 0 e −i ( K •r −ωt )   & & − (α& • r& ) −i ( β& •r& −ωt )   E = E 0 e e   & & & & & − (α& •r& ) & & [cos( β • r − ω t ) = Re[ E ] = E 0 Re[e − j ( K •r −ωt ) ]     E 0 e & & & & & & &   ( β • r0 − ω t ) = ( β • r − ω t ) Ÿ β • ( r − r0 )   & & & & & & &   (α • r0 ) = (α • r ) Ÿ α • (r − r0 )  

  E

=

  v

ω β cos(ψ )

&   E ( x, y , z , t ) = &

 

1

+∞+∞ +∞

+∞

(2π )4 −³∞−³∞−³∞³−∞

  E ( k x , k y , k z , ω )e

& i ( xk + yk + zk +ωt ) E (k x , k y , k z , ω )e x y z dxdydzdω  

i ( xk x + yk y + zk z +ωt )

& & & = E (k x , k y , k z , ω )e i ( K •r +ωt )  

&

' & = E × H   & & & & & & ∂D & ∂B = 0     ∇ • P − j • E − E • −H• ∂t ∂t   P

&& & & ∂ §1 & 2· §1 & 2· P n dS = j • E d τ + ε E d τ + ¨ ¸ ¨ μ H ¸ dτ   ³³S ³³³ ³³³ ³³³ ¹ ¹ τ τ ©2 τ ∂t © 2 & &   I λ = v (λ ) P (λ )  

 

&

780 nm & & 1 jλt ( ) ( ) v λ P λ e d λ = v(λ ) P(λ )e jλt dλ   ³−∞ ³ 2π 380 nm & &   Φ = ³³ I • n dS  

  I

=

1 2π

S

  Φ

Ω2 & & & & & = ³³ I • n dS = ³³ I • n sin(θ )dθdφ = ³ I (Ω) dΩ   S

Ω1

S

& dΦ I (Ω ) =   dΩ & dΦ   I (Ω) =   dΩ

 

φ2 θ2 & &   Φ = ³³ I • n dS = ³ dφ ³ I (θ , φ ) sin(θ ) dθ   S

φ1

θ1

& & I   L = L ′ &   I




(OHPHQWLGL)RWRPHWULD,QGLFHGHOOHHTXD]LRQL

  L( x, y , z ,Ď&#x2C6; )

=

dÎŚ I =   cos(Ď&#x2C6; ) dS dΊ cos(Ď&#x2C6; ) dS

Ď&#x20AC; 2 dÎŚ   = 2Ď&#x20AC; Âł L cos(Ď&#x2C6; ) sin(Ď&#x2C6; ) dĎ&#x2C6;   dS 0

Ď&#x20AC; 2

= 2Ď&#x20AC;L Âł cos(Ď&#x2C6; ) sin(Ď&#x2C6; ) dĎ&#x2C6; = Ď&#x20AC;L  

  Lu

0

  E

=

  1 sb

dÎŚ dΊ I â&#x2039;&#x2026; = I â&#x2039;&#x2026; cos(Ď&#x2C6; ) = cos(Ď&#x2C6; )   dS dS r 2 =

  1 phot

cd cd cd = â&#x2C6;&#x2019; 4 2 = 10 4 2 = 10 4 nt   2 cm 10 m m =

lm lm lm = â&#x2C6;&#x2019; 4 2 = 10 4 2 = 10 4 lux   2 cm 10 m m

1 cd cd â&#x2030;&#x2026; 0,318 2   2 Ď&#x20AC; m m

  1 asb

=

  1 L

1 cd 10 4 cd = = 10 4 asb   2 2 Ď&#x20AC; cm Ď&#x20AC; m

=

  1mmL

= 10 â&#x2C6;&#x2019;3 L = 10mL = 10asb =

10 cd   Ď&#x20AC; m2

  1

cd 1 cd 1 cd 10 4 cd cd â&#x2030;&#x2026; = = â&#x2030;&#x2026; 10,76 2   2 2 â&#x2C6;&#x2019;4 2 2 930,27 cm 930,27 10 m 930,27 m ft m

  1

cd 1 cd cd â&#x2030;&#x2026; â&#x2030;&#x2026; 0,1548 2   2 2 6,4609 cm inch cm

lm 10 4 lm lm â&#x2030;&#x2026; 10,76 2     1 2 â&#x2030;&#x2026; 2 930,27 m ft m   1

lm 1 lm lm â&#x2030;&#x2026; â&#x2030;&#x2026; 0,1548 2   2 2 6,4609 cm inch cm

  1 fL =

1 cd   Ď&#x20AC; ft 2

  1 fL

=

§ 10 4 cd ¡ 1 cd 10,76 cd â&#x2C6;&#x2019;4 ¨¨ ¸ = 10,76 10 â&#x2C6;&#x2019;4 L = 1,076mL   â&#x2030;&#x2026; = 10 10 , 75 2 ¸ Ď&#x20AC; ft 2 Ď&#x20AC; m2 Ď&#x20AC; m Š š

  1 fL

=

1 cd 10,76 cd cd â&#x2030;&#x2026; â&#x2030;&#x2026; 3,4262 2   2 2 Ď&#x20AC; ft Ď&#x20AC; m m




(OHPHQWLGL)RWRPHWULD,QGLFHGHOOHHTXD]LRQL

  I = αLS  







BBBBBBBBBBBBBBBBBBBBBBBBBBBBBB























 

Elementi di Fotometria  

Elmenti di Fotometria

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