2 Concepts Concave and convex mirrors Converging and diverging lenses FocusConverging and diverging lensesLens equationEye as an optical instrumentFar and near pointsCorrective lenses
3 Lenses Convex lens bulges out –converges light Concave lens caves in –diverges light
4 Focus Light goes through – focal points on both sides – F and F’ Always a question which focal point to choose when ray tracingConverging lens:Parallel beam of light is converged in 1 point – focal point FReal focus: f>0Key for the focal point choice: Rays must bend inDiverging lens:Parallel beam of light seems to be coming out of 1 point FVirtual focus: f<0Key for the focal point choice: Rays must bend out
5 Ray tracing for converging lens 3 Easy rays:Parallel through focus FThrough focus F’ parallel (reversible rays)Through the center itself
9 Image formed by a diverging lens ) Object between F and lensVirtual Erect Larger than object Behind the object on the same side of the lensImage formed by a diverging lense) Object at FCharacteristics of the image regardless of object postion Virtual Erect Smaller than object Between object and lens
10 Diverging lens Same rules, but remember to diverge (bend out) Parallel projection through focus FProjection through F’ parallelThrough the center goes through
11 Lens equation P – power of lens, in Dioptry (D=1/m) f must be in m d0 – distance to objectdi – distance to imagef –focusP – power of lens, in Dioptry (D=1/m)f must be in m
12 Sign convention for lenses and mirrors h0>0di>0 – real imageOpposite side from Odi<0 - virtual imageSame side with Ohi>0 – upright imagehi<0 - inverted imagef>0 – concave mirrorf<0 – convex mirrorf>0 – converging lensf<0 – diverging lenshi>0di<0 – upright image is always virtualhi<0di>0 – inverted image is always real
13 Images in lenses and mirrors Converging lens, concave mirrord0>2f – (real, inverted), smaller2f>d0>f – (real, inverted), largerd0<f – (virtual, upright), largerDiverging lens, convex mirrorImage is always(virtual, upright), smaller.
14 System of lensesImage of the 1st lens of object for the 2nd lens.
15 Spherical mirrors Convex mirror bulges out – diverges light Concave mirror caves in – converges light
16 FocusParallel beam of light (e.g. from a very distant object) is converged in 1 point – focal point FDistance from the mirror to F is called focal distance, or focusf =r/2
17 Ray tracing 3 Easy rays: Parallel through focus Through focus parallel (reversible rays)Through the center of curvature C itself
23 Eye as an optical instrument Eye is a converging lensCiliary muscles are used to adjust the focal distance.f is variableImage is projected on retina – back plane.di stays constantImage is real (light excites the nerve endings on retina) inverted (we see things upside-down)di>0, hi<0Optic nerves send ~30 images per second to brain for analysis.
24 Far and near points for normal eye Relaxed normal eye is focused on objects at infinity – far pointf0=eye diameter =~2.0 cmNear point – the closest distance at which the eye can focus - for normal eye is ~25cm. Adjusted focus:f1=1.85 cm
25 Corrective lenses Farsighted eye Nearsighted eye Nearsighted eye far point<infinitydiverging lens f<0 P<0Farsighted eyenear point > 25 cmconverging lens f>0 P>0Lens+eye = system of lensesCorrective lenses create virtual, upright image (di<0 !) at the point where the eye can comfortably seeFarsighted eyeNear point = 70 cm di =-0.70mNeed to correct near pointObject at “normal near point” =25cmNearsighted eyeFar point = 17 cm di =-0.17mNeed to correct far pointObject at “normal far point” =infinity
26 Images in lenses Converging lens - for farsighted d0>2f – (real, inverted), smaller2f>d0>f – (real, inverted), largerd0<f – (virtual, upright), largerDiverging lens - for nearsightedImage is always (virtual, upright), smaller.Image in corrective lenses is always virtual and uprightdi<0 and hi>0
27 Corrective lenses Nearsighted eye Far point = 17cm Near point = 12 cm new near point -?Diverging lens projects infinity to 17 cm from the eye
28 Real and virtual image Mirrors: I and O – same side opposite sides I O Real, invertedlight goes throughVirtual, uprightlight does not go throughOMILenses:I and O –opposite sidessame sideReal, invertedlight goes throughOLIVirtual, uprightlight does not go throughOIL