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PHY122_L19_PostingAfterLecture

PHY122_L19_PostingAfterLecture - PHY122 Physics for the...

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PHY122 – Physics for the Life Sciences II Lecture 19 Ray Optics, continued HW 11 due Sunday, 13 Nov. at 8 pm Note: Clicker Channel 21 11/10/2011 Lecture 19 1 Post-lecture note added: Prof. Koch ended the lecture on 10 Nov. with slide 26 in this file. Please go over slides 27-29 for your HW11 due Sunday, 13 Nov. and again before Lec. 20 on 15 Nov. Prof. Koch will cover them quickly at the beginning of Lec. 20.
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Lecture 19 2 Geometric / Ray Optics Angles are measured with respect to the normal n to surface of reflection or to interface of refraction the incident ray, the outgoing ray (reflected or refracted), and the normal to the surface/interface all lie in the same plane for RE FLECT ION: n inc = n refl barb4right θ inc = θ refl for RE FRACT ION: n inc sin θ inc = n refr sin θ refr 11/10/2011 Snell’s Law (or Descarte’s Law)
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medium 1 n 1 medium 2 n 2 > n 1 Calculation & answer from last lecture Medium 1 is air ( n 1 = 1.00 ) Calculate the index of refraction n 2 of medium 2 … 11/10/2011 Lecture 19 3 1 1 2 2 sin sin n n θ θ = ( ) ( ) 1 90 45 sin si 90 n 55 n = ° - ° ° - ° 0.7071 1.00 1.23 0.5736 = = 1 2 2 1 sin sin n n θ θ = g2016 g2869 g2016 g2870 In Ray Optics angles must be measured from the NORMAL to the interface
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Some indices of refraction 11/10/2011 Lecture 19 4 at fixed wavelength Dispersion: n = n( λ ) n varies with wavelength
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Lecture 19 5 Flat Mirrors A Flat Mirror is the simplest optical element Rules, Image Construction, and Definitions: O BJECT (unprimed symbols) DISTANCE s > 0 (positive if rays EMERGE from the object TOWARDS the mirror; normally always positive) image BEHIND the mirror barb4right VIRTUAL (primed symbols) image, IMAGE DISTANCE s’ <0 From construction: • Mirror: s’= –s ; h’= +h – definitions: image on same side as object: s’> 0 ( real image) image on other side from object: s’< 0 ( virtual image) – MAGNIFICATION: m h’ / h= –s’ / s= + 1 (flat mirror) s object image θ inc θ refl 11/10/2011 s’ h’ h
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air glass Lecture 19 6 Color Dispersion The index of refraction of a material depends on the material properties (e.g. on the density) as well as on the wavelength λ of the light; – for most materials n de creases with in creasing wavelength in the visible spectrum , – i.e. violet / blue light is more refracted than red light the variation n ( λ ) is called dispersion : responsible for the spectral color separation in the rainbow, stemming from refraction-reflection-refraction in small raindrops causes the colored edges in cheap optical instruments the prototypical spectral analyzer is the PRISM: 11/10/2011
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glass: n inc air: n refr < n inc Lecture 19 7 Total Internal Reflection A curious phenomenon occurs when light impinges on an glass-air interface (i.e. from inside the glass into air), i.e. when n inc >n refr : Snell’s Law: sin θ refr = sin θ inc n inc / n refr In creasing the angle of incidence , see the figure below, such that: sin θ inc n inc / n refr becomes 1 • Clearly sin θ refr cannot become larger than 1 barb4right NO REFRACTION for: and for θ inc θ critical ALL the light is REFLECTED – e.g., glass ( n =1.5 )
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