Total Internal Reflection
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1 Total nternal Reflection Consider light moving from glass (n.5) to air (n.) i r n sin n sin n n incident ra r refracted ra reflected ra GLASS AR sin n sin n >.e., light is bent awa from the normal. as gets bigger, gets bigger, but can never get bigger than 9!! > n general, if sin > (n / n ), we have NO refracted ra; we have TOL NTRNAL RFLCTON. sin c n /n For eample, light in water which is incident on an air surface with angle > c sin - (./.33) 8.8 will be totall reflected. This propert is the basis for the optical fiber communication. Total nternal Reflection Total internal reflection occurs when > c and provides % reflection. This has better efficienc than silvered mirror. amples of devices using Critical Angle Fiber Optic Network Maps Prism Binoculars Fiber Optics Fiber optics is etremel important for high speed nternet and digital data transfer at long distances. Man companies (Lucent) have laid fiber over long Distances to provide internet service. Fiber optics has replaced copper for long distance communication and is becoming increasingl used for local communications. Lecture, ACT : Critical Angle Lecture, ACT : Critical Angle An optical fiber is surrounded b another dielectric. n case this is water, with an inde of refraction of.33, while in case this is air with an inde of refraction of.. Compare the critical angles for total internal reflection in these two cases Case Case c c water n.33 glass n.5 water n.33 air n. glass n.5 air n. An optical fiber is surrounded b another dielectric. n case this is water, with an inde of refraction of.33, while in case this is air with an inde of refraction of.. Compare the critical angles for total internal reflection in these two cases Case Case c c water n.33 glass n.5 water n.33 air n. glass n.5 air n. a) c > c b) c c a) c > c b) c c n n Since n >n TR will occur for > critical angle. Snell s law sas sin c n /n. c) c < c c) c < c n >n f n., then c is as small as it can be. So c > c.
2 Polariation Consider our M plane wave. The field is polaried in the Y-direction. We sa this is linearl polaried light. UP ο fast slow f λ/ s RCP sin( k ωt) B sin( k ωt) c Most light sources are not polaried in a particular direction. This is called unpolaried light or radiation. polaroid (sunglasses) Long molecules absorb - field parallel to molecule. (transmission ais) M wave; energ and intensit Previousl, we demonstrated the energ densit eisted in fields in Capacitor and in B fields in inductors. We can sum these energies, u ε + B μ Since, cb and c / με then u in terms of, u ε + ε + ε ε μ c > M wave has energ and can transport energ at speed c M wave; ntensit The intensit,, is the energ flow per unit area. n Y&F, section 3., the average for a sinusoidal plane wave (squared) is worked out, ε c ma Y&F section 3. ct A Suppose we have transverse and B fields moving, at velocit c, to the right. f the energ densit is u ε and the field is moving through area A at velocit c, the energ in volume Act, uact, passes through. Hence the amount of energ flow per unit time per unit surface area is, du ( uact) uc ε c A dt At Cell Phone Problem 3.8) A sinusoidal electromagnetic wave emitted b a cell phone has a wavelength of 35. cm and an electric field amplitude of 5. - V/m at a distance of 5 m from the antenna. (a) The intensit? (b) The total average power? a.) ε c ; (8.85 C 8 / Nm )(3 m / s)( W / m 6 V / m) b.) Assume isotropic: P/A; Pπr π (5m) P 3 W LP ntensit Reduction UP (unpolaried light) LP?? LP?? This set of two linear polariers produces LP light. What is the final intensit? First LP transmits / of the unpolaried light: / Second LP projects out the -field component parallel to the : cos cos Law of Malus nˆ
3 3 Preflight 3 An M wave polaried along the -ais, is incident on two orthogonal polariers. Yes adding an intermediate polarier will restore some light!!! 5) What percentage of the intensit gets through both polariers? a) 5% A polarier at an intermediate angle can change the direction of polariation so that some light is able to get through the last filter. b) 5% c) % 6) s it possible to increase this percentage b inserting another polarier between the original two? plain. Lecture 3, ACT Light of intensit, polaried along the direction is incident on a set of linear polariers as shown. Assuming, what is, A the intensit at the eit of the polariers, in terms of? (b) (c)? Lecture 3, ACT Light of intensit, polaried along the direction is incident on a set of linear polariers as shown. Assuming, what is, A the intensit at the eit of the polariers, in terms of? (b) (c) ˆn ˆn? B What is the relation between and 3, the final intensities in the situation above when the angle and 3, respectivel? < 3 (b) 3 (c) > 3 3? 3? We proceed through each polarier in turn. The intensit after the first polarier is: cos ( ) The electric field after the first polarier is LP at. The intensit after the second polarier is: cos ( 9 ) Lecture 3, ACT Light of intensit, polaried along the direction is incident on a set of linear polariers as shown. Assuming, what is the A relation between the, the intensit at the eit of the polariers, in terms of? (b) (c) B ˆn What is the relation between and 3, the final intensities in the situation above when the angle and 3, respectivel? < 3 (b) 3 (c) > 3 n general, the first polarier reduces the intensit b cos, while the second polarier reduces it b an additional factor of cos (9 ). Thus, the final output intensit is given b: out cos ( ) cos ( 9 ) cos ( ) sin ( ) sin ( ) This has a maimum when. ˆn? Polariation b reflection unpolaried n a n b Medium b i The reflected ras are partiall polaried in the horiontal plane. The transmitted ras are also partiall polaried. i r Can alwas describe in terms of components in two arbitrar directions. The components are equal for unpolaried light.
4 Polariation b reflection n a n b Medium b p p From Mawell s eqn. it can be shown that Brewster s angle is given b r n tan b p na For a certain angle, the Brewster angle, the reflected light is completel polaried in the horiontal plane. This occurs when the angle between the refl. and refr. ras is 9 o. Light reflected on dashboard to the windshield will be polaried in the horiontal plane. Using polaroid dark glasses with a vertical ais will remove most of reflected light Polariation b Scattering Suppose unpolaried light encounters an atom and scatters (energ absorbed & reradiated). What happens to the polariation of the scattered light? The scattered light is preferentiall polaried perpendicular to the plane of the scattering.» For eample, assume the incident unpolaried light is moving in the -direction.» Scattered light observed along the -direction (scattering plane -) will be polaried along the -direction.» Scattered light observed along the -direction (scattering plane -) will be polaried along the -direction. This bo contains atoms which scatter the light beam lectric field lines from oscillating dipole full computer simulation - a snapshot in time Dipole radiation pattern Oscillating electric dipole generates e-m radiation that is linearl polaried in the direction of the dipole Radiation pattern is doughnut shaped & outward traveling ero amplitude above and below dipole maimum amplitude in-plane Applications Sunglasses The reflection off a horiontal surface (e.g., water, the hood of a car, etc.) is strongl polaried. Which wa? A perpendicular polarier can preferentiall reduce this glare. Polaried sk The same argument applies to light scattered off the sk: Polariing filters important in photograph!
5 5 The inde of refraction depends on frequenc, due to the presence of resonant transition lines. For eample, ultraviolet absorption bands in glass cause a rising inde of refraction in the visible, i.e., n(higher ω) > n(lower ω): n red.5 n blue.53 Dispersion: n n(ω) Rainbows nde of refraction white light.5 ultraviolet.5 absorption bands.5 frequenc prism Split into Colors Rainbows Wh is the sk blue? Light from Sun scatters off of air particles Raleigh scattering Raleigh scattering is wavelength-dependent. Shorter wavelengths (blue end of the visible spectrum) scatter more. This is also wh sunsets are red! At sunset, the light has to travel through more of the atmosphere. f 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).
θ =θ i r n sinθ = n sinθ
θ i = θ r n = 1 sinθ1 n sin θ Total Internal Reflection Consider light moving from glass (n 1 =1.5) to air (n =1.0) n 1 incident ray θ 1 θ r reflected ray GLASS sinθ sinθ 1 > 1 = n n 1 θ > θ 1 n θ refracted
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