F winter 2008 lecture 6 18 19 1 2 3 4 draw an

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Unformatted text preview: UCSD: Physics 121; 2008 Using the focus condition real foci s= s’ = f Tracing an arbitrary ray (positive lens) virtual foci s= s’ = f s=f s’ = s= f s’ = s= s’ = f s= s’ = f Winter 2008 Lecture 6 18 19 1. 2. 3. 4. draw an arbitrary ray toward lens stop ray at middle of lens note intersection of ray with focal plane from intersection, draw guiding (helper) ray straight through center of lens (thus undeflected) undeflected) 5. original ray leaves lens parallel to helper why? because parallel rays on one side of lens meet each other at the focal plane on the other side Winter 2008 20 5 Geometrical Optics 01/31/2008 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Tracing an arbitrary ray (negative lens) Image Formation 1. draw an arbitrary ray toward lens 2. stop ray at middle of lens 3. draw helper ray through lens center (thus undeflected) parallel undeflected) to the incident ray 4. note intersection of helper with focal plane 5. emerging ray will appear to come from this (virtual) focal point why? parallel rays into a negative lens appear to diverge from the same virtual focus on the input side • Place arrow (object) on left, trace through image: – 1) along optical axis (no defl.); 2) parallel to axis, goes through far focus with optical axis ray; 3) through lens center; 4) through near-side focus, emerges parallel to optical axis; 5) arbitrary ray with helper • Note convergence at image position (smaller arrow) – could run backwards just as well Winter 2008 21 Winter 2008 22 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Notes on Image Formation Virtual Images • If the object is inside the focal length (s < f): • Note the following: – a virtual (larger) image is formed – non-inverted – image is inverted – image size proportional to the associated s -value: ray 3 proves it – both s and s ’ are larger than f ( s = 120; s’ = 80; f = 48) • Ray numbers are same procedure as previous • This time s’ is negative: – s = 40; f = 60; s ’ = 1 20 – negative image distances indicate virtual images • Gaussian lens formula (simple form): Winter 2008 Lecture 6 23 Winter 2008 24 6 Geometrical Optics 01/31/2008 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 The lens-maker’s formula lens-maker’ Deriving Gaussian Formula from Rays • We saw the Gaussian lens formula before: – f is positive for positive lenses, negative for negative lenses – s is positive on left, s ’ is positive on right • But in terms of the surface properties: – – – – • • • • R1 is for the left surface (pos. if center of curvature to right) R2 is for right surface (pos. if center of curvature to right) bi-convex (as in prev. examples) has R 1 > 0; R2 < 0 n is the refractive index of the material (assume in air/vac) Winter 2008 Object has height, h; image height = h’ tangent of ray 3 angle is h/s, so h’ = h(s’/s) ray 2 angle is h/f, so h’ = ( h/f) (s’ f) set the two expressions for h’ equal, and divide by hs’ hs – the result will pop out • can do the same trick using virtual images too 25 Winter 2008 26 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Lenses map directions into displacements Telescope • A telescope has an “objective” lens and an eyepiece objective” • Two objects at infinity an angle distinct spots separated by – following geometry, = f·tan – sharing a focal plane; giving the eye the parallel light it wants apart produce apart • Everything goes as...
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This note was uploaded on 01/30/2014 for the course PHYS 121 taught by Professor Staff during the Winter '08 term at UCSD.

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