TERMINOLÓGIA A JEDNOTKY OPTICKÉHO ŽIARENIA
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1 TERMINOLÓGIA A JEDNOTKY OPTICKÉHO ŽIARENIA OEaLT Prednáška 2
2 Rádiometrické a fotometrické veličiny iny a jednotky Rádiometrická Fotometrická veličina symbol jednotka veličina sym -bol jednotka Energia žiarenia Q e J Svetelná energia Q v lm.s Žiarivý tok (výkon) Φ e W Svetelný tok Φ v lm Ožiarenie E e W.m -2 Osvetlenie E v lx Intenzita žiarenia Žiarivosť I e W.sr -1 Intenzita osvetlenia Svietivosť I v cd lm.sr -1 Žiarenie (vyžarovanie) M e W.m -2 Svetlenie M v lm.m -2 Merná žiarivosť L e W.sr -1.m -2 Merná svietivosť- Jas L v cd.m -2 lx nt
3 Definicie veličín n a jednotiek Definicie veličín: Φ = dq/dt E = dφ/da M = dφ/da I = dφ/dω L = d 2 Φ/dA.dΩ cosα = dm/dω cosα Definicie jednotiek: lx = lm. m -2 (Lux) Osvetlenie cd = lm.sr -1 (Kandela) Intenzita osvetlenia nt = cd.m -2 (Nit) Jas
4 Rádiometrické veličiny Energia žiarenia charakterizuje elektromagnetické pole a udáva množstvo žiarenia. označuje sa Q e [J] Žiarivý tok vyjadruje výkon prenášaný žiarením. označuje sa Φ e [W] Φ = dq e e dt Ožiarenie udáva podiel žiarivého toku vyžiareného zdrojom na jednotku plochy označuje sa E e [W.m -2 ] dφ e Ee = da Intenzita žiarenia udáva podiel žiarivého toku vyžiareného zdrojom v smere do elementárneho priestorového uhla a veľkosti tohto priestorového uhla dφ označuje sa I e [W.sr -1 e ] I e = d pre hodnotu priestorového uhla platí Ω d Ω = da 2 r Φ e E e A = 1m 2 Ω = 1sr r = 1m
5 Rádiometrické veličiny Žiarenie predstavuje žiarivý tok Φ e na jednotku plochy A, ktorá žiarivý tok vyžaruje alebo rozptyľuje po ožiarení iným zdrojom žiarenia (žiarenie vyžaruje) označuje sa M e [W.m -2 ] M e = dφ da Merná žiarivosť je žiarivý tok vyžarovaný alebo rozptyľovaný z povrchu materiálu s jednotkovou plochou A do priestoru ohraničeného jednotkovým priestorovým uhlom Ω. označuje sa L e [W.sr -1 m -2 ] L e = 2 d Φ e dω da cos Θ e
6 Spektrálne vlastnosti žiarenia Celkový tok žiarenia: Φ e = Φ eλ dλ 0 (W) Monochromatický tok žiarenia: Φ eλ = dφ d λ e (W.m-1)
7 Veličiny iny charakterizujúce ce zdroj svetla Svetelný tok Φ v [lm] Svetelná účinnosť K = Φ v Φe Monochromatická svetelná účinnosť K vλ λ = Φ Φe λ
8 Veličiny iny charakterizujúce ce zdroj svetla Ľudské oko - citlivosť závisí na vlnovej dĺžke, maximum pre denné videnie pri vlnovej dĺžke 555 nm je K M = 680 lm/w, maximum pre nočné videnie pri vlnovej dĺžke 507 nm je K M = 1740 lm/w. Pomerná sveteľná účinnosť V λ Vlnová dĺžka [nm] pre denné videnie pre nočné videnie Pomerná svetelná účinnosť ľudského oka je definovaná ako: Svetelný tok je potom možné určiť zo vzťahu: Φ v = V λ = K λ K M K M V λ Φe λ dλ 0 [lm]
9 Lambertov kosínový zákonz Pre žiarivú energiu emitovanú rovinným povrchom je intenzita žiarenia I (W/sr) určená kosínusom uhla medzi smerom dopadu a kolmicou k povrchu (platí pre Lambertovské resp. difúzne povrchy). I = I N.cos φ (W/sr) Φ [w], I[cd] o φ r r A I A = I N E A [lx] B I B = I N.cos φ E B [lx] E = dφ/da I = dφ/dω
10 Fotónový tok Fotónový tok -dn p /dt (fotóny/s) Počet fotónov je určený podielom celkovej energie žiarenia Q e k energii jednotlivého fotónu Q p : N p = Q e /Q p = Q e. λ / h.c (fotóny) Počet fotónov pri energii žiarenia 1 Joule potom bude: N p = λ. 5, (fotóny, nm) Fotónový tok možno vyjadriť nasledovne : d N dt p = dq dt e 15. λ.5, = Φe. λ, (fotóny/s, W, nm)
11 Zákony absolútne čierneho telesa Planckov distribučný zákon Tento zákon určuje spektrálne rozdelenie žiarenia absolútne čierneho telesa: c1 1 M ( T) = 2 eλ [ W/m. µ m] 5 C2 λ λt e + 1 c 1 = 2π c 2 h = 3, [ W. µ m /m ] c 2 = hc k =1, [ µ m.k] kde c 1 a c 2 sú Planckove konštanty žiarenia absolútne šierneho telesa a M eλ určuje vyžarovanie do priestorového uhlu 2π steradiánov.
12 Zákony absolútne čierneho telesa Planckov distribučný zákon Tento zákon určuje spektrálne rozdelenie žiarenia absolútne čierneho telesa:
13 Zákony absolútne čierneho telesa Keďže absolútne čierne teleso je Lambertovský (difúzny) zdroj a jeho žiarenie je konštantné vo všetkých smeroch, platí L = M/λ a teda aj: L = 2c 2 h 1 λ W / m m.sr λ 2 λkt e 1 ( ) [ 2 T. µ ] 5 c Planckov zákon môže byť vyjadrený tiež ako fotónový tok dosadením vzťahu pre energiu fotónu: ( ) [ 2 fotónov / s.m m] h c. µ 4 M T = λ 2 π c λ 1 λ kt e 1
14 Zákony absolútne čierneho telesa Wienov posuvný zákonz Vlnová dĺžka maxima vyžarovania absolútne čierneho telesa je nepriamo úmerná jeho absolútnej teplote.
15 Zákony absolútne čierneho telesa Wienov posuvný zákonz
16 Zákony absolútne čierneho telesa Stefan - Boltzmanov zákon Celkové žiarenie absolútne čierneho telesa je dané súčinom Stefan-Boltzmanovej konštanty a štvrtej mocnine jeho teploty: M = σ T 4 [ W m -2 ] σ - Stefan-Boltzmanova konštanta σ = J s 1 m 2 K 4
17 Zákony absolútne čierneho telesa Color Wavelength interval Frequency interval violet ~ 380 to 430 nm ~ 790 to 700 THz blue ~ 430 to 500 nm ~ 700 to 600 THz cyan ~ 500 to 520 nm ~ 600 to 580 THz green ~ 520 to 565 nm ~ 580 to 530 THz yellow ~ 565 to 590 nm ~ 530 to 510 THz orange ~ 590 to 625 nm ~ 510 to 480 THz red ~ 625 to 740 nm ~ 480 to 405 THz The spectrum of visible light in nanometers
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