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Chapt23_VG2

# Chapt23_VG2 - Lenses Thin Lenses Ray Tracing Thin Lenses...

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Lenses

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Thin Lenses: Ray Tracing
Thin Lenses: Ray Tracing

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Thin Lenses: Ray Tracing Real Image
y d(y) Thin lens approximation D=2a d << D , f d ( y ) = a 2 y 2 2 L Lens has parabolic thickness Determines focal length We would like to show that all rays, independent of the point they pass through the lens, y, focus to the same point f.

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What is the phase of a wave arriving at the focus? Wave crests φ = k ( n 1) d ( y ) + r ( y ) [ ] Contribution from lens Contribution from region between lens and focus d k = 2 π / λ vac y r ( y ) = y 2 + f 2 Wave phase
φ = k ( n 1) d ( y ) + r ( y ) [ ] Phase d ( y ) = a 2 y 2 2 L Recall thickness of lens Phase is independent of ray (y) if ( n 1) y 2 2 L + y 2 2 f = 0 r ( y ) = y 2 + f 2 f + y 2 2 f Approximate y << f 1 f = ( n 1) L Focal length determined by curvature of lens and index of refraction Some Math

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Graphically locating an image and determining it’s size h h = s s = m
A.The image will be inverted and blurry.

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