Optics-Problem-4-11.doc - 4-11 By finding appropriate expressions for k ． r write equations describing a sinusoidal plan wave in three dimensions

# Optics-Problem-4-11.doc - 4-11 By finding appropriate...

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4-11 By finding appropriate expressions for r k , write equations describing a sinusoidal plan wave in three dimensions, displaying wavelength and velocity, if propagation is a. along the +z-axis b. along the line x=y, z=0 c. perpendicular to the planes x+y+z=constant Ans: a. ) )( / 2 sin[( ) sin( ˆ ) ( ˆ ) / 2 ( vt z A r k A k vt z r k k  b. )] 2 )( / 2 sin[( ) sin( ) ˆ ˆ )( 2 ( ] ˆ ) 2 ( ˆ ) 2 [( ) ˆ ˆ )( / 2 ( vt x A r k A j i vt x y x j t v y i t v x r j i k y x  c. ] ) ( 3 3 ) / 2 sin[( )] 3 3 3 3 3 3 )( / 2 sin[( ]} ˆ ) 3 3 ( ˆ )

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• Fall '17
• William Heywood

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