Polarization Diffraction Hydrogen Atom Spectrum a Polarized Beam Brewster’s law Diffraction Pattern, Single Slit, double slit Diffraction Grating Circular Apertures Balmer Series and Planck’s Constant

Intensity of a Polarized Beam The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as –I = I max cos 2 θ I o is the intensity of the polarized wave incident on the analyzer This is known as Malus’s law and applies to any two polarizing materials whose transmission axes are at an angle of θ to each other

Polarization by Reflection The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θ p Brewster’s law relates the polarizing angle to the index of refraction for the material θ p may also be called Brewster’s angle

Diffraction Pattern, Single Slit The diffraction pattern consists of the central maximum and a series of secondary maxima and minima The pattern is similar to an interference pattern

Two-Slit Diffraction Patterns The conditions for the first diffraction minimum a sin θ = λ

Diffraction Grating The condition for maxima is –d sin θ bright = mλ m = 0, ±1, ±2, … The integer m is the order number of the diffraction pattern If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle

Circular Apertures The diffraction pattern of a circular aperture consists of a central bright disk surrounded by progressively fainter bright and dark rings The limiting angle of resolution of the circular aperture is –D is the diameter of the aperture

Absorption Spectroscopy An absorption spectrum is obtained by passing white light from a continuous source through a gas or a dilute solution of the element being analyzed The absorption spectrum consists of a series of dark lines superimposed on the continuous spectrum of the light source

Balmer Series In 1885, Johann Balmer found an empirical equation that correctly predicted the four visible emission lines of hydrogen –H α is red, λ = nm –H β is green, λ = nm –H γ is blue, λ = nm –H δ is violet, λ = nm

Emission Spectrum of Hydrogen The wavelengths of hydrogen’s spectral lines can be found from –R H is the Rydberg constant R H = x 10 7 m -1 –n is an integer, n = 3, 4, 5,… –The spectral lines correspond to different values of n h=6.6361× J-sec Planck’s Constant

Energy-level Diagram for the H atom n=  n=1 n=2 n=3 n=4 n=5 n=6 … 3889 Å 3970 Å 4103 Å 4340 Å 4861 Å 6563 Å 萊曼系列 (Lyman Series) ( 紫外光區 ) 巴爾麥系列 (Balmer Series) ( 可見光區、近紫外光區 ) 帕申系列 (Paschen Series) 布拉克系列 (Brackett Series) Lyman series: Paschen series: Brackett series: