OPTI 201R 10 L14

# OPTI 201R 10 L14 - 14-1 5.6 Gaussian Equation of a Single...

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OPTI 201R Fall 2010 14-1 5.6 Gaussian Equation of a Single Surface Figure 5.9 Paraxial ray trace……again!!! nn n u nu y R ! " #\$ !! %" &’ () (5.29) ! Rewrite the paraxial refraction equation as a function of the object distance, z, and the image distance, z "# z y u z y u ! % ! " " % ; * + R y n n z ny z y n " ! " " % ! " ! (5.31) * + R n n z n z n " ! , % ! ! (5.32) * + - % " ! R n n , % ! ! z n z n (5.34) * Therefore, in the paraxial region, the refraction equation is actually independent of ray height.

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OPTI 201R Fall 2010 14-2 “What radius for a glass rod is necessary to form an image inside the glass at 37.5cm for an object 50cm away from the curved surface (n=1.5)?” From the stated problem, we know that: * + * + R cm cm R n n z n z n cm z cm z n 1 5 . 1 50 1 5 . 37 5 . 1 5 . 37 ; 50 ; 5 . 1 " , " % " ! , % ! ! , % ! " % % ! Solving for R : * + * +* + * + * + * +* + * + cm R cm cm cm cm cm cm cm cm R 333 . 8 1 5 . 37 50 5 . 1 1 5 . 1 50 50 50 1 5 . 37 50 5 . 1 1 5 . 1 50 50 1 5 . 37 5 . 1 1 5 . 1 % , " % , " % , " % Also : * + cm m m R R R n n Diopters m m z n z n 33 . 8 0833 . 6 5 . 6 1 5 . 1 6 50 . 1 375 . 5 . 1 % % % % " % " ! % % " " % , % ! ! - NOTE: R is positive, so the surface is convex. Example 5.3
OPTI 201R Fall 2010 14-3 5.7 Focal Lengths and Focal Points Back Focal Point, Back Focal Length ! The back focal point F* is the on-axis point where the image of an object at infinity (z = - \$% ’( located. - The wavefronts are planar for an object at infinity… - …therefore the rays in object-space are parallel to the z-axis… - …therefore… ! The back focal point F* is the point where rays from infinity (parallel to the optical axis) in object space cross the optical axis in the next space.

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## This note was uploaded on 08/23/2010 for the course OPTICS 201R taught by Professor Staff during the Spring '10 term at Arizona.

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OPTI 201R 10 L14 - 14-1 5.6 Gaussian Equation of a Single...

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