Determination of Reflected And Transmitted Fields By Geometrical Optics Ii
Determination of Reflected And Transmitted Fields By Geometrical Optics Ii
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Hence the equation (l) with? = <> and ^=^<'^'^ yield the raapp-lng of i^'v' on the tangent plane to ;'^^ on a parallel plane "by means of reflected or trans- mitted rays. As mentioned in the introduction and shown I the Jacobian J of the inverse mapping, evaluated at the origin, determines the area ratio neces- sary to compute the amplitude of the reflected or transmitted field. This Jacobian is given by: (2) or , „ r' - J . IfM-t) ;f(:^)] mw -^/fyi/f/ Equation (3) Is Q-btained from Sq. (2) Ijy performing the indicated differentiations m Eq. (1) and substitution into Eq. (2) remem-berinfi that these partial derivatives are to "be evalxiated at the origin. 3, Calculation of the Jacohian In order to compute the Jacobian presented in Eq. (3) we rauat first evaluate the components of T and its partial derivatives at the origin. These ■become: V ^ ^ J "Ti ^ ^ ; % ^ SlI ^ 4; "hero 2>4f^^ Jit) - ^. ^ /^ - ajMf -y^## -fS/ 6 j^ H , o{$jS ^A. '^ JL -^l] These expressions involve the partial derlvatives^
What to read after Determination of Reflected And Transmitted Fields By Geometrical Optics Ii?
You can find similar books in the "Read Also" column, or choose other free books by Joseph B Keller to read online
To quickly assess the difficulty of the text, read a short excerpt:
Hence the equation (l) with? = <> and ^=^<'^'^ yield the raapp-lng of i^'v' on the tangent plane to ;'^^ on a parallel plane "by means of reflected or trans- mitted rays. As mentioned in the introduction and shown I the Jacobian J of the inverse mapping, evaluated at the origin, determines the area ratio neces- sary to compute the amplitude of the reflected or transmitted field. This Jacobian is given by: (2) or , „ r' - J . IfM-t) ;f(:^)] mw -^/fyi/f/ Equation (3) Is Q-btained from Sq. (2) Ijy performing the indicated differentiations m Eq. (1) and substitution into Eq. (2) remem-berinfi that these partial derivatives are to "be evalxiated at the origin. 3, Calculation of the Jacohian In order to compute the Jacobian presented in Eq. (3) we rauat first evaluate the components of T and its partial derivatives at the origin. These ■become: V ^ ^ J "Ti ^ ^ ; % ^ SlI ^ 4; "hero 2>4f^^ Jit) - ^. ^ /^ - ajMf -y^## -fS/ 6 j^ H , o{$jS ^A. '^ JL -^l] These expressions involve the partial derlvatives^
What to read after Determination of Reflected And Transmitted Fields By Geometrical Optics Ii?
You can find similar books in the "Read Also" column, or choose other free books by Joseph B Keller to read online
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