PHY132_L28 - Classical Physics II Classical Physics II...

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lassical Physics II Classical Physics II PHY132 Lecture 28 Curved Mirrors Lecture 28 1 04/14/2010
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Geometric / Ray Optics much older than the discovery of the wave nature of light. empirical facts: etween a source and a receiver light moves along straight lines between a source and a receiver light moves along straight lines (“rays”) in a given uniform material – at interfaces (reflective, refractive) the direction of the ray hanges in predictably: changes in predictably: angles: measured w.r.t. the normal n to the surface of reflection or to the interface of refraction icture: picture: – the incident ray, the outgoing ray (reflected or refracted), and the normal to the surface/interface all lie in the same plane or E RACT ON: Lecture 28 2 – for RE FRACT ION: n inc sin θ inc = n refr sin θ refr –for RE FLECT ION: n inc = n refl θ inc = θ refl 04/14/2010
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Total Internal Reflection A curious phenomenon occurs when light impinges on an glass-air interface, e when i.e. when n inc >n refr : – Snell’s Law: sin θ refr = sin θ inc n inc / n refr – Increasing the angle of incidence, see the Figure below, such that: ote: the thickness sin θ inc n inc / n refr 1 i.e. 1 > sin θ inc n refr / n inc : • Clearly sin θ refr cannot become larger than 1 NO REFRACTION for: sin θ inc n refr / n inc sin θ critical Note: the thickness of the rays indicates their relative intensity air: n refr < n inc •a n d f o r θ inc θ critical ALL the light is REFLECTED g: θ refr θ refr θ refr =90° n glass: n inc – e.g.: glass ( n =1.5 ) air ( n =1.0 ): θ critical = arcsin( n refr / n inc ) θ c θ inc = θ crit θ refl θ refl Lecture 28 3 = arcsin(0.67) = 42° 04/14/2010 θ inc θ refl
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Applications the efficient transmission of light through fibers (fiber- optics) is a very important application of the phenomenon of TOTAL INTERNAL REFLECTION: – as long as all incident angles remain over the critical angle, the light is efficiently “piped” down the fiber… f course some absorption may be present Of course, some absorption may be present… – glass fibers are thin, highly flexible, cheap, and immune to electrical interference! odulated light can carry lots of information (now >1 Bit s) – modulated light can carry lots of information (now >1 GBit/s) Lecture 28 4 04/14/2010
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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 decreases with increasing wavelength in the visible spectrum , e iolet lue ght is fracted an d ght i.e. violet / blue light is more refracted than red light –the var iat ion n ( λ ) is called dispersion : • responsible for the spectral color separation in the rainbow, stemming rom refraction- flection- efraction in small raindrops from refraction reflection refraction in small raindrops • causes the colored edges in cheap optical instruments – the prototypical spectral analyzer is the PRISM: air glass Lecture 28 5 04/14/2010
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