Prozorov_31 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURES 31 Dispersion. Interference. Young’s experiment. what defines a color? So the atom oscillates with the frequency of the radiation and then re-emits. Frequency remains the same Wavelength changes n1 v1 c 1 f n1f n2 < n1 v2 c 2 1 f n2f “Color” correspond to a fixed frequency. The wavelength depends on the medium. PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 2 Dispersion Light refraction is wavelength dependent. This effect is made more pronounced if the index of refraction is higher. PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 3 example: Dispersion White light shone into a prism Dispersion: Different frequencies of color have different indexes of refraction in glass. n(f) A. nred > nblue B. nred < nblue C. Insufficient info Blue rays bend further from original direction than red rays nblue is further from 1 than nred. PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 4 This might be easier to understand (with one refraction only): Blue rays bend further from original direction than red rays nblue is further from 1 than nred. PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 5 a famous example of light dispersion PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 6 dispersion and rainbows The red comes from the higher droplets and the blue from the lower (as we have seen in the wavelength dependence of light refraction). PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 7 Huygens’s Principle o From the work of Christian Huygens in 1678, the geometrical analysis reveals that every point of a wave front can be considered to be a source of secondary wavelets that spread with a speed equal to the speed of propagation of the wave. PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 8 Huygen’s law All points on a wavefront serve as point sources of secondary wavelets in this example spherical wavefronts add up to straight wavefront PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 9 Huygens’s Principle II o Huygens’s work can form an explanation of reflection and refraction. PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 10 Law of reflection (from Huygen’s) Wavefront at t1 Reflected wavefront at t4 c 3Δt c 3Δt t2 =t1 +Δt t3 =t1 +2Δt t4 =t1 +3Δt Isosceles triangle angles must be the same PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 11 Law of refraction (from Huygens) Wavefront at t1 θ1 n1 n2 θ1 θ2 θ2 Refracted wavefront at t4 θ1 v2t t2 =t1 +Δt t3 =t1 +2Δt t4 =t1 +3Δt v1t θ2 PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University v1t v2t sin 1 sin 2 sin 2 v2 n1 sin 1 v1 n2 7 November 2011 12 Fermat’s principle Light will take the path that takes the least time. A θi B θr Several paths from A to B going through mirror surface The shortest path for reflection is the path where θi = θr Similarly for refraction, the shortest path is the one that satisfies Snell’s law! PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 13 interference Interference works like for any wave: at any given point, the E/B field is the vector sum of the E/B field from each wave. Constructive In phase (or out of phase by whole λ) Destructive Out of phase by λ/2 PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 14 path difference ΔL At point P: P r2 Constructive interference L r1 r2 m S2 r1 S1 m 0, 1, 2... Destructive interference 1 L r1 r2 m 2 m 0, 1, 2... Two monochromatic coherent light sources PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 15 Coherence S1 and S2 are two sources of monochromatic, coherent light. The phase difference between these two sources is constant. Light is produced by millions of atoms emitting at the same time, with random phases two light sources are in general incoherent Easy trick to produce coherent light: split a beam in two. PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 16 Young’s experiment Light and dark alternating fringes r2 Monochromatic light r1 Max: L r1 r2 m m 0, 1, 2... • • • Waves start off in phase at two slits Travel different distances to screen Relative phase at screen PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 17 Dark Bright Dark Bright Dark Dark Bright PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 18 PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 19 Position of maxima/minima R d Parallel if R >> d L d sin Bright fringes: d sin m m 0, 1, 2... Dark fringes: 1 2 d sin m PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University m 0, 1, 2... 7 November 2011 20 Intensity for two slit interference If R >> d, the E fields of each ray are parallel at point P R Time dependence of E field at point P : E1 E 0 cos t E2 E 0 cos t with k L k r2 r1 E total 2E 0 cos cos t E max cos cos t 2 2 Amplitude for resultant wave Intensity I E 2 max IP Imax cos 2 2 PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University Imax = intensity at θ = 0, where phase difference is ϕ = 0 7 November 2011 21 IP Imax cos 2 2 All maxima should have the same intensity. But this is what is observed… This is a diffraction effect. Back to this in a couple of lectures. PHYS222 - Lecture 31 - Prof. Ruslan Prozorov - Iowa State University 7 November 2011 22 ...
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