Class2

Class2 - Refraction from Fermats principle Q A OB OB = x AQ...

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Refraction from Fermat’s principle Q Q’ O B A x OB = x p AO = h AQ = ' ' h B Q = 1 d QO = 2 ' d O Q = 2 2 1 1 d n d n + = Optical path length: = 0 ) ( δ There is only one variable in the problem; why? Fermat’s principle: = 0 dx d 2 2 1 1 sin sin θ = n n
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Example I: Atomic Force Microscope
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Example II: refraction of divergent rays
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Refraction of divergent paraxial rays
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Refraction by a prism Prism: two refracting surfaces that make an angle α with each other. A ray entering a prism (index of refraction n) will be deflected from its original direction by an angle δ , known as angular deviation. α δ n N1 N2
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Finding δ ) ( ) ( 2 2 1 1 i t t i θ ϕ β δ + = + = β ϕ N1 N2 Air: n’=1 Why? 2 1 i t α + = + = 2 1 t i ) sin( ) sin( 1 1 1 t i n = ) sin( 1 ) sin( 2 2 t i n = See Hecht p.187 () ( ) [ ] + = cos sin sin sin sin 1 2 1 1 2 2 1 1 i i i n
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Dispersing Prisms The prism is one of the most important optical elements, it can serve as beam splitter, polarizer, dispersion tool and interferometer. Example: Dispersing Prism (used in optical spectrum analyzer) Dispersion refers to the frequency (i.e. wavelength) dependence of index of refraction n( ω ) . This implies that the speed of light in a dispersive medium is also a function of frequency (or wavelength),
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This note was uploaded on 10/19/2009 for the course PHY 31 taught by Professor Cebe during the Fall '08 term at Tufts.

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Class2 - Refraction from Fermats principle Q A OB OB = x AQ...

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