Refraction and Reflectance: Understanding the Interaction of Light with Different Media, Slides of Analytical Chemistry

Download Refraction and Reflectance: Understanding the Interaction of Light with Different Media and more Slides Analytical Chemistry in PDF only on Docsity! Reflection = EM strikes a boundary between two media differing in η and bounces back Specular reflection = situation where angle of incidence (θi) equals angle of reflection (θr) Medium 1 (air) η = 1.00 Medium 2 (glass) η = 1.50 Incident ray θ1 θ2 Reflected ray docsity.com Ir (η2 - η1)2Reflectance = R = ---- = -------------- Ii (η2 + η1)2 Where Ii and Ir = incident & reflected intensity For radiation going from air (η = 1.00) to glass (η = 1.50) as shown in previous slide R = 0.04 = 4 % Many surfaces at 4 % each (i.e., many lenses) can cause serious light losses in a spectrometer. This generates stray radiation or stray light. docsity.com Critical Angle (ФC) Normal to surface Medium 1 (air) Medium 2 (glass) Incident ray is 90o to normal this is called grazing incidence Ф1 Ф2 Refracted ray Maximum value of Ф2 Ф2 = ФC At 90o incidence sin Ф1 = 1.0 η1sin ФC = -----η2 Important for: 1) Refractometers 2) Fiber Optics docsity.com Critical Angle (ФC) Normal to surface Medium 2 (air) Medium 1 (glass) Ф2 Ф1 Incident ray Maximum value of Ф1 for Refraction Ф1 = ФC When incidence is at the Critical angle, refraction is at 90o η2sin ФC = -----η1 Important for: 1) Refractometers 2) Fiber Optics Refracted ray docsity.com Critical Angle (ФC) Normal to surface Medium 2 (air) Medium 1 (glass) Ф2 Ф1 Incident ray New value of Ф1 for Reflection Ф1 > ФC At angles greater than the Critical angle, 100 % reflection occurs or Total Internal Reflectance Important for: 1) Refractometers 2) Fiber Optics Refracted ray Reflected ray docsity.com Linearly polarized light oscillates in one plane only as it moves through space Here E vector is vertically polarized and H vector is at 90o in horizontal plane docsity.com Circularly polarized light rotates in either a left handed or right handed spiral as it moves through space Here E vector is circularly polarized and H vector follows, but is offset by 90o docsity.com Combining equal beams where one is right circularly polarized and the other left, results in linearly polarized radiation Polarization is particularly important for studying optically active materials using - Optical Rotatory Dispersion (ORD) - Circular Dichroism (CD) - Fluorescence Polarization docsity.com 1) Absorption dN ------ = N1 B12 ρ(ν)dt 2) Spontaneous Emission – goes back down spontaneously dN ------ = N2 A21dt Rate of Absorption Number of atoms/molecules in state 1 Einstein probability coefficient Spectral volume density (i.e., radiation density term) Einstein coefficient going from state 2 to 1 No ρ(ν) term docsity.com 3) Stimulated Emission - photon strikes state 2 causing it to emit dN ------ = N2 B21 ρ(ν)dt Relationship between probability coefficients B12 = B21Absorption Stimulated Emission A21 = 8 π h σ3 B12 docsity.com Boltzmann Distribution – relative population of states 1 & 2 is dependent on energy difference and temperature at equilibrium N1 e-E1/kT----- = ----- N2 e-E2/kT K = Boltzmann’s constant (8.62 x 10-5 eV/oK) T = absolute temperature (298 oK = 25 oC) An additional term is add to the right side of the equation if there is more than one state with the same energy = degeneracy docsity.com Quantitative Aspects of Absoption Beer-Lambert Law (or Beer’s Law) IoA = log ---- = ε b C I I T = ---- %T = T x 100 Io Io = measured source intensity I = measured intensity after absorption Intensity change does not change absorbance Absorbance Transmittance molar absorptivity concentration path length docsity.com Effects other than absorption that reduce source intensity (i.e., scattering, reflection) may also be measured as absorbance and must be accounted for when measuring I & Io Incident Beam Reflection Loses Reflection Loses Cuvette Transmitted Beam Light loses occur due to: 1) reflection at boundaries 2) scattering by molecules or particles 3) absorption which is process of interest scatter docsity.com • Absorbance & Transmittance are unitless • If C is mol/L & b is in cm then ε is L/mol-cm • To minimize the effect of light loses from reflection the procedure followed in UV-vis spectrophotometry is to measure Io with a reference blank of pure solvent in the light path & then measure I under the same conditions – cuvettes should be optically matched if using 2 & clean, free of scratches, lint, fingerprints, etc. docsity.com Assumptions made in deriving Beer’s Law: 3) Pathlength is the same over the volume being measured – this becomes a problem with round cells λ varies across the bandwidth so some wavelengths pass through more solution than others (b varies) The consequence is the same as for polychromatic radiation = curved response Round cell Light beam detector Different components of the incident beam are absorbent with different efficiencies docsity.com 4) The nature of the absorber does not change with concentration – a variety of effects can cause this assumption to break down, e.g. dimerization, acid-base or complexation equilibria docsity.com All of the above mentioned deviations from Beer’s Law (or instrumental deviations) are really only deviations in the sense that the experimental conditions deviate from the conditions that have been assumed in deriving Beer’s Law Beer’s Law always holds docsity.com