Understanding Polarization and Reflection of Electromagnetic Waves, Study notes of Physics

Download Understanding Polarization and Reflection of Electromagnetic Waves and more Study notes Physics in PDF only on Docsity! 1 Lecture 48 – Electromagnetic waves Chapter # 33 • Review • Radiation pressure • Polarization • Reflection and refraction 2 Review • Electromagnetic waves: Maxwell Eqs. • Speed of electromagnetic waves • E x B : direction of travel of the wave - Poynting vector smc /458,792,2991 00 == εμ 2 00 rmsEc SIBES μμ =≡×= 11 rrr )(/2/2 )sin( lengthwavecTck tkxEE m === −= ωππλ ω c B E B E tkxBB m m m == −= )sin( ω 5 Polarization • Natural light: unpolarized (Fig 33-11) Polarized light: fields (E, B) oscillate in a single plane (Fig 34-10) 6 Unpolarized Light • We have primarily been considering light that has a definite polarization (e.g., linear or circular). Most sources – a candle, the sun, any light bulb – produce light that is unpolarized : – it does not have a definite direction of the electric field – there is no definite phase between orthogonal components – the atomic or molecular dipoles that emit the light are randomly oriented in the source – the intensity of light transmitted through a polarizer is always half the intensity of the unpolarized input, regardless of the orientation of the polarizer (though of course the output is polarized!) These are all equivalent ways of describing the same thing. • How else can we produce linearly polarized (LP) e-m waves? – Absorp./reflect. of vector component of wave perp to “polarizer” microwave source (polarized) TA (transmission axis) LP slotted metal plate The E-field component parallel to the slots is absorbed and/or reflected. The E-field component perpendicular to the slots is transmitted. Long molecules absorb E-field parallel to molecule. TA (transmission axis) • polaroid (sunglasses) • Absorption produces LP e-m waves but in so doing it also reduces intensity of the wave. How much?? Linear Polarization LP Intensity Reduction • This set of two linear polarizers produces LP light. What is the final intensity? – First LP transmits 1/2 of the unpolarized light: I1 = 1/2 I0 – Second LP projects out the E-field component parallel to the TA: θcos12 EE = 2EI ∝ θ212 cosII = This result is called the Law of Malus (for LP light incident on LP) ( )nnEE ˆˆ12 •= rr UP (unpolarized light) TA LP E1 θ E2 θ I=I0 I1=?? I2=?? TA LP n̂ 11 Sample Problem 33-3 Fig. 34-16a shows a system of three polarizing sheets in the path of initially polarized light. The polarizing direction of the first sheet is parallel to the y axis, that of the second sheet is 60o counterclockwise from the y axis, and that of the third sheet is parallel to the x axis. What fraction of the initial intensity I0 of the light emerges from the system, and how is that light polarized? θ20 cosII = 02 1 II = 01 2 1 II = 2 60cos60cos 2 160cos 2 0 2 0 2 12 o oo IIII =⎟ ⎠ ⎞ ⎜ ⎝ ⎛== 0 22 0 2 2 0 2 23 094.0 2 30cos60cos 30cos 2 60cos30cos II III oo o o o == ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ == 094.0 0 3 = I I o30 12 Polarization by Scattering • Suppose unpolarized light encounters an atom and scatters (energy absorbed & reradiated). – What happens to the polarization of the scattered light? – The scattered light is preferentially polarized perpendicular to the plane of the scattering. x y z • For example, assume the incident unpolarized light is moving in the z- direction. • Scattered light observed along the x-direction (scattering plane = x-z) will be polarized along the y-direction. • Scattered light observed along the y-direction (scattering plane = y-z) will be polarized along the x-direction. This box contains atoms which “scatter” the light beam 15 Geometric Optics • So far EM waves in vacuum • What happens to EM waves (usually light) in different materials? – we must include κ in Maxwell’s Equations -----> index of refraction, n. • Restriction: waves whose wavelength is much shorter than the objects with which it interacts. • Pretend that light propagates in straight lines, called rays. • Our primary focus will be on the REFLECTION and REFRACTION of these rays at the interface of two materials. incident ray reflected ray refracted ray MATERIAL 1 MATERIAL 2 16 Reflection and Refraction • Geometrical Optics - light travels in straight line (Fig 33-17): incident, reflected, and refracted rays • Angles of: – incidence θ1 – reflection θ’1 – refraction θ2 • Index of refraction (Table 33-1) v cn = 17 Reflection and Refraction • Law of reflection: – Reflected ray lies in the plane of incidence • Law of refraction (Fig 33-18): – Refracted ray lies in the plane of incidence 11' θθ = 1122 sinsin θθ nn = 20 • How are Maxwell’s eqns in matter different? ε 0 → ε ≡ ε 0 κ μ0 → μ ≈ μ0 (for most materials) • Therefore, the speed of light in matter is related to the speed of light in vacuum by: • The wave incident on an interface can not only reflect, but it can also propagate into the second material. • The speed of an electromagnetic wave is different in matter than it is in vacuum. – Recall, we derived from Maxwell’s eqns in vacuum: The index of refraction is frequency dependent: For example, in glass nblue = 1.53 nred = 1.52 Index of Refraction 00 1 εμ =c n cv = where n = “index of refraction” of the material: 1κ≈ >n 0 0 1 1 cv με μ ε κ κ = ≈ ≡ 21 Chromatic Dispersion • Index of refraction varies with wavelength (Fig 33-19, 33-20): blue refracted more than red 22 Dispersion In de x of re fra ct io n frequency ultraviolet absorption bands 1.50 1.52 1.54 Ultraviolet absorption bands cause a rising index of refraction in the visible white light prism Split into Colors 25 Checkpoint 33-5 Which of the drawings here (if any) show physically possible reflection? 1122 sinsin θθ nn = (a) Yes (b) No (c) No 26 Total Internal Reflection • See Fig 33-24 • Critical angle • Application: optical fibers )(sin 90sinsin 1 21 0 21 anglecrirtical n n nn c c −= = θ θ 27 Total Internal Reflection • Consider light moving from glass (n1=1.5) to air (n2=1.0) I.e., light is bent away from the normal. as θ1 gets bigger, θ2 gets bigger, but θ2 can never get bigger than 90° !! In general, if sin θ1 > (n2 / n1), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION. For example, light in water which is incident on an air surface with angle θ1 > θc = sin-1(1.0/1.5) = 41.8° will be totally reflected. This property is the basis for the optical fibers used in communication. incident ray reflected ray refracted ray θ2 θ1 θr GLASS AIRn2 n1 1 sin sin 2 1 1 2 >= n n θ θ 121 θθ > 30 Checkpoint 33-6 Suppose the prism in this sample problem has the index of refraction n = 1.4. Does the light still totally internally reflect if we keep the incident ray horizontal but rotate the prism (a) 10o clockwise and (b) 10o counterclockwise in Fig. 34-26? 31 Why is the sky blue? • Light from Sun scatters off of air particles–“Rayleigh scattering” – Rayleigh scattering is wavelength-dependent. – Shorter wavelengths (blue end of the visible spectrum) scatter more. • This is also why sunsets are red! – At sunset, the light has to travel through more of the atmosphere. – If longer wavelengths (red and orange) scatter less… – The more air sunlight travels through, the redder it will appear! – This effect is more pronounced if there are more particles in the atmosphere (e.g., sulfur aerosols from industrial pollution).