RADIATION LAWS

WHY STUDY ABOUT RADIATION ? INFORMATION RECEIVED FROM A SATELLITE ABOUT THE EARTH AND ITS ATMOSPHERE COMES IN THE FORM OF EM RADIATION IT IS THEREFORE NECESSARY TO UNDERSTAND THE MECHANISMS BY WHICH THIS RADIATION IS GENERATED AND HOW IT INTERACTS WITH THE ATMOSPHERE

BASIC QUANTITIES EM RADIATION CONSISTS OF ALTERNATING ELECTRIC AND MAGNETIC FIELDS ELECTRIC FIELD VECTOR IS PERPENDICULAR TO THE MAGNETIC FIELD VECTOR DIRECTION OF PROPAGATION IS PERPENDICULAR TO BOTH OF THEM RADIATION IS OFTEN SPECIFIED BY ITS WAVELENGTH, WHICH IS THE DISTANCE BETWEEN CRESTS OF THE ELECTRIC OR MAGNETIC FIELD. Electrical Field Radiation Source Magnetic Field

Electromagnetic Waves

Period, Amplitude and Wavelength

FREQUENCY, WAVELENGTH AND AMPLITUDE OF A WAVE Frequency 3 Hz t =1 sec t =0 Wavelength Amplitude Wavelength – Distance between two successive crests or troughs Frequency - Number of wavecrests passing a fixed point in one second Amplitude - Height of the crest from mid point

EM SPECTRUM FREQUENCY AN ALTERNATE WAY TO DESCRIBE RADIATION, IS THE RATE AT WHICH THE ELECTRIC OR MAGNETIC FIELD OSCILLATES WHEN OBSERVED AT A POINT. THE FUNDAMENTAL UNIT OF FREQUENCY IS THE HERTZ (Hz), OR ONE CYCLE PER SECOND. THE FREQUENCY IS RELATED TO THE WAVELENGTH()  = c /  WAVENUMBER(). IS THE RECIPROCAL OF THE WAVELENGTH. IT IS EXPRESSED IN cm-1. DIRECTLY PROPORTIONAL TO FREQUENCY.

ELECTROMAGNETIC SPECTRUM WAVELENGTH Cosmic Rays 1 picometer or less (1pm=10-12m) Gamma Rays 1 -100 pm X Rays 100 pm – 10nm (1nm = 10-9m) UV 10 - 400 nm Visible 400 -700nm IR 0.7 – 1000 µm (1 µm = 10-6m) Microwaves 1mm – 30 cm ( Freq 300 – 1 GHz)

EM SPECTRUM A BROAD RANGE OF WAVELENGTHS FROM ULTRAVIOLET TO THE MICROWAVE REGION IS USEFUL IN SATELLITE METEOROLOGY.

EM SPECTRUM 0.4 0.5 0.6 0.7

EM ENERGY A FUNDAMENTAL PROPERTY OF THE EM RADIATION IS THAT IT CAN TRANSPORT ENERGY. MANY OF THE UNITS USED TO QUANTIFY EM RADIATION ARE BASED ON ENERGY. THE BASIC UNIT OF THE RADIANT ENERGY IS THE joule RADIANT FLUX. IS RADIANT ENERGY PER UNIT TIME, MEASURED IN watts [W; joules per second (J s-1)] RADIANT FLUX DENSITY. IS RADIANT FLUX CROSSING A UNIT AREA. IT IS MEASURED IN watts per square metre (W m-2) RADIANT EXITANCE(M). IS RADIANT FLUX DENSITY EMERGING FROM AN AREA, AND IRRADIANCE (E) IS RADIANT FLUX DENSITY INCIDENT ON AN AREA

BLACKBODY AN IDEAL SURFACE HAVING THE FOLLOWING PROPERTIES ABSORPS ALL INCIDENT RADIATION REGARDLESS OF WAVE LENGTH AND DIRECTION NO SURFACE EMITS MORE ENERGY THAN A BLACK BODY BLACKBODY IS A DIFFUSE EMITTER

QUANTUM NATURE OF EM RADIATION 1905- EINSTEIN EXPLAINED PHOTO ELECTRIC EFFECT IN TERMS OF EMISSION OF ONE ELECTRON DUE ABSORPTION OF ONE UNIT OF ‘QUANTUM’ OF RADIANT ENERGY MAX PLANCK PROPOSED ENERGY ‘Q’ OF A ‘QUANTUM’ IS PROPORTIONAL TO FREQUENCY Q = h  where h = 6.6256 x 10-34 Joules Sec

PLANK’S BLACKBODY RADIATION LAW RADIANCE EMITTED BY A BLACKBODY IS GIVEN BY B(T) = 2 h c2 -5 / [exp(hc / kT) – 1] h is the Planck’s constant = 6.6256  10 -34 W s2 c is the velocity of light = 2.997925  10 8 m s-1 K is the Boltzmann’s constant = 1.38054  10 -23 W s K-1 T is the absolute temperature in degree K &  is the wavelength in m.   PLANCK FUNCTION IS MORE CONVENIENTLY WRITTEN AS B(T) = C1 -5 / [exp(C2/ T) – 1] WHERE C1 & C2 ARE THE FIRST AND SECOND RADIATION CONSTANTS

PLANK’S BLACKBODY RADIATION LAW B(T) IS A MONOTONICALLY INCREASING FUNCTION OF T FOR A PARTICULAR WAVELENGTH  = , IT T1 IS LESS THAN T2, THEN B(T1) < B(T2) B(T) HAS A SINGLE MAXIMUM AT THE WAVELENGTH

WEIN’S DISPLACEMENT LAW By differentiating Planck’s law we can get another useful relation,  max T = 2898 m K   where  max is the wavelength at which the radiant flux emitted by the blackbody is the maximum.

The radiant exitance from Spectral distribution at the top of the atmosphere for solar irradiance and earth’s emission. Sun T ~6000K, Earth T ~300K The radiant exitance from sun and earth follows Planck’s equation [ ] 1 e C M T 5 2 - l = 104 1000 Sun max = 2898 T mm Radiant exitance (W m-2 mm-1) 100 Earth 10 1 0.1 0.5 1 10 Wavelength (mm) Taking T = 5777K for Sun,  max = 0.50 m and T=300K for Earth,  max = 9.66 m

STEFAN - BOLTZMANN LAW ANOTHER IMPORTANT ASPECT OF THE PLANK FUNCTION IS ITS INTEGRAL OVER WAVELENGTH. THE TOTAL EXITANCE FROM A BLACKBODY IS MBB = 0∫ WHERE  IS CALLED THE STEFAN BOLTZMANN CONSTANT AND THE EXPRESSION IS CALLED STEFAN - BOLTZMANN LAW   B(T) d =  T 4

RAYLEIGH – JEANS APPROXIMATION IN MICROWAVE REGION, C2/T << 1 THUS exp(C2/T) CAN BE APPROXIMATED BY 1 + C2/T. THE PLANK FUNCTION THEN BECOMES B(T) = (C1/C2) -4 T THIS IS KNOWN AS THE RAYLEIGH – JEANS APPROXIMATION. IT SAYS THAT IN THE MICROWAVE PORTION OF THE SPECTRUM, RADIANCE IS SIMPLY PROPORTIONAL TO TEMPERATURE

BRIGHTNESS TEMPERATURE IN THE MICROWAVE REGION, IT IS CUSTOMARY TO DIVIDE RADIANCE VALUE BY (C1/C2) -4 AND REFER TO THE QUOTIENT AS BRIGHTNESS TEMPERATURE BRIGHTNESS TEMPERATURE WHEN USED IN INFRARED PORTION OF THE SPECTRUM, WE CALL IT AS EQUIVALENT BLACKBODY TEMPERATURE

NON-BLACKBODIES  +  +  = 1 SINCE REAL MATERIALS ARE NOT PERFECTLY BLACK, A WAY MUST BE DEVISED TO QUANTIFY HOW CLOSELY IT APPROXIMATES A BLACKBODY. THE EMITTANCE OF BODY IS DEFINED AS  = EMITTED RADIATION AT WAVELENGTH () / B(T) EMITTANCE CAN BE FUNCTION OF TEMPERATURE AND VIEWING GEOMETRY AS WELL AS WAVELENGTH. FOR A BLACKBODY, IS IDENTICALLY ONE. THREE RELATED QUANTITIES DESCRIBE THE FATE OF RADIATION INCIDENT ON A BLACKBODY ABSORPTANCE () = ABSORBED RAD. AT  / B(T) REFLECTANCE () = REFLECTED RAD.AT  / B(T) TRANSMITTANCE () = TRANSMITTED RAD. AT  / B(T). BECAUSE THESE THREE PROCESSES ARE THE ONLY POSSIBILITIES FOR THE INCIDENT RADIATION, BY ENERGY CONSERVATION, EACH QUANTITY MUST BE BETWEEN ZERO AND ONE  +  +  = 1

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