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Review: Self-inductance Announcements •WebAssign HW Set 8 due this Friday •Problems cover material from Chapters 22 •Only 3 more HW assignments left Self-inductance: ε = −L RL Circuits: • The second midterm exam is coming – Monday, Nov 8 •Will cover from 18.1 thru 22.7 •Room assignments TBA QUESTIONS? PLEASE ASK! Time constant: Current: I = ε R τ = ΔI Δt L=N ΔΦ B NΦB = ΔI I L R (1 − e ) −t / τ Energy stored in an inductor: PEL = ½ L I 2 Review: Electromagnetic Waves Light is an EM wave c= Speed of light All EM waves obey c = ƒλ E and B are transverse EM waves carry energy: 1 μ oε o c = “Bibliotheque Nationale de France” http://alikaragoz.net/geometric-reflection/ E B Average power per unit area = u⎞ ⎛ fo ≈ fs ⎜ 1 ± ⎟ c⎠ ⎝ Chapter 22 "Perfect Portage Reflection“ http://www.alaska-in-pictures.com/perfect-portage-reflection-1218-pictures.htm 2 E B E2 c Bmax I = max max = max = 2μo 2μo c 2 μo EM waves carry momentum For complete absorption of energy U, p=U/c For complete reflection of energy U p=(2U)/c EM spectrum The Doppler effect for EM waves Reflection and Refraction of Light u⎞ ⎛ fo ≈ fs ⎜1 ± ⎟ c⎠ ⎝ 1 22.2: Geometric Optics – Using Ray Approximation 22.1: Dual Nature of Light Light! It’s a wave? It’s a particle? It’s both! Some characteristics are explained by wave nature of light, some are explained better by particle nature Experiments display either the wave nature OR the particle nature of light Very different from other particles; eg, they have no mass Light travels in a straight line in homogeneous media until it encounters a boundary between two different media The ray approximation is used to represent beams of light ‘Particles’ of light Æ ‘photons’ Rays are perpendicular to wave fronts Photon energy E = h ƒ h = 6.63 x 10-34 J s (Planck’s constant) Refraction of Light Reflection of Light; Law of Reflection A ray of light, the incident ray, travels in a medium When a light ray encounters a boundary, part of the incident ray is reflected back We deal with specular reflection in this course Law of Reflection normal - line perpendicular to the surface at the point where the incident ray strikes the surface The incident ray makes an angle of θ1 with the normal The reflected ray makes an angle of θ1’ with the normal The angle of reflection is equal to the angle of incidence: θ1= θ1’ When a light ray encounters a boundary: Specular and diffuse reflection A ray of light is an imaginary line drawn along the direction of travel of the light beams A wave front is a surface passing through points of a wave that have the same phase and amplitude The ray that enters the second medium is refracted (bent) at the boundary part of the ray is reflected part of the ray enters the second medium The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane Refracted occurs because the speed of light is different in the two media The angle of refraction depends upon the material and the angle of incidence: sin θ12 vv22 sin = = constant sinθθ21 vv1 sin 2 Refraction of Light When a light ray encounters a boundary: part of the ray is reflected part of the ray enters the second medium The ray that enters the second medium is refracted (bent) at the boundary Refraction of Light The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane Refracted occurs because the speed of light is different in the two media The angle of refraction depends upon the material and the angle of incidence: n= Some values of n speed of light in a vacuum c = speed of light in a medium v For a vacuum, n = 1 For other media, n > 1 n is a unitless ratio As the value of n increases, the speed of the wave decreases As light travels from one medium to another, its frequency does not change The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane Refracted occurs because the speed of light is different in the two media The angle of refraction depends upon the material and the angle of incidence: sin θ12 vv22 sin = = constant sinθθ21 vv1 sin The Index of Refraction The index of refraction, n, of a medium can be defined: part of the ray is reflected part of the ray enters the second medium The ray that enters the second medium is refracted (bent) at the boundary sin θ12 vv22 sin = = constant sinθθ21 vv1 sin When a light ray encounters a boundary: Index of Refraction Extended The frequency remains the same as the wave travels from one medium to the other v=ƒλ The ratio of the indices of refraction of the two media can be expressed as various ratios c n1 n2 λ1 v1 = = = c n1 λ2 v2 n2 3 Snell’s Law of Refraction Some Indices of Refraction n1 sin θ1 = n2 sin θ2 θ1 is the angle of incidence θ2 is the angle of refraction Can derive from Maxwell equations Problem 22.21, p 755 Two light pulses are emitted simultaneously from a source. The pulses take parallel paths to a detector 6.20 m away but one moves through air and the second through a block of ice. Determine the difference in the pulses’ arrival times at the detector. 22.4: Dispersion The index of refraction in anything except a vacuum depends on the wavelength of the light This dependence of n on λ is called dispersion The index of refraction for a material usually decreases with increasing wavelength (‘normal’ dispersion) Dispersion plays a very important role in fiber optical communications Snell’s Law indicates that the angle of refraction made when light enters a material depends on the wavelength of the light In ‘anomalous’ dispersion, the index of refraction increases with increasing wavelength Violet light refracts more than red light when passing from air into a material 4 Refraction in a Prism The amount the ray is bent away from its original direction is called the angle of deviation, δ Since all the colors have different angles of deviation, they will spread out into a spectrum Violet deviates the most Red deviates the least 5