), separating three materials of index of refraction n 1

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Reginald Henderson
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1 Thi Leses A les is a otical device cosistig of two refractig surfaces The simlest les has two sherical surfaces close eough together that we ca eglect the distace betwee the surfaces (i.e., thi) Cosider two sherical surfaces (with radii of curvature ad ), searatig three materials of idex of refractio,, ad 3 For the first surface, we ca use the refractig surface euatio to relate the object distace, image distace, ad radius of curvature, igorig the secod surface.

2 From diagram (o board), we get Now let the image formed by surface, I, be the object for surface, O I is a virtual image. Therefore Here, we eglect the thickess of the les Agai aly the refractig surface euatio, but for surface, eglectig surface The image, I, is real

3 Let 3 (air or vacuum) ad Addig with ad, gives Lettig ad f gives This is the les maker s euatio!! " # $ $ % &!! " # $ $ % & ) ( ) ( f

4 Examle Problem If a swimmig ool full of water is.00 m dee. How far below the to of the water surface does the bottom aear whe viewed from above? Examle Problem The rojectio les i a certai slide rojector is a sigle thi les. A slide 4.0 mm high is to be rojected so that its image fills a scree.80 m high. The slide-to-scree distace is 3.00 m (a) Determie the focal legth of the rojectio les. (b) How far from the slide should the les of the rojector be laced i order to form the image o the scree?

5 Aberratios I our develomet of the mirror ad les euatios, we assumed araxial rays, i.e. rays with small agles with resect to the ricial axis We also assumed for leses that they are thi These are aroximatios (but reasoable) For more recise determiatios of images, we must use the laws of refractio ad reflectio to trace the aths of rays We fid that two tyes of aberratios result from the use of sherical surfaces

6 Sherical Aberratios A geometrical issue for rays of the same λ ays further from the ricial axis are focused closer to the les for a covergig les Sherical aberratio ca be elimiated by the use of, for examle, arabolic mirrors all rays focus to a commo oit but exesive Or aertures ca be used to remove the oaraxial rays

7 Hubble s sherical aberratio Before Fixed

8 Chromatic Aberratio Sice the idex of refractio is a fuctio of λ, rays with differet λ will refract at differet agles whe assig through a les (for the same araxial ray) The rays focus at differet locatios for each λ Not a roblem for moochromatic light beams For ordiary (olychromatic) light, chromatic aberratio ca be reduced by - materials with miimal λ deedece o - use combiatios of divergig ad covergig leses

Otical Devices: The Camera The camera system cosists of a covergig les, aerture, shutter, ad CCD is adjusted to focus a real, iverted image o the CCD for large

9 Otical Devices: The Camera The camera system cosists of a covergig les, aerture, shutter, ad CCD is adjusted to focus a real, iverted image o the CCD for large object distace (>>) The shutter is oeed for a time duratio Δt. Usually, betwee /30 to /50 s exosure time. This allows light to strike the CCD creatig the image. CCD

10 The itesity of the light reachig the CCD is roortioal to the area viewed by the camera ad the effective area of the les cotrolled by the diameter D of the aerture) Light itesity I is the rate of light eergy received by the CCD er uit area (eergy/area/time) Whe >>f ad f, the area of the image is f. Therefore, I is roortioal to D /f. I hotograhy, the light-gatherig caability of a les is exressed i terms of f/d called the f- umber. Therefore I ( f umber) Icreasig D by reduces f-umber by / ad icreases I by at the CCD

11 Tyical f-umbers f/, f/.8, f/4, f/5.6, f/8, f/, f/6 large small aerture (exosure) The followig combiatios give same exosure f/4 & /500s f/5.6 & /50s f/8 & /5 s Examle Problem A camera is beig used with a correct exosure at f/4 ad a shutter seed of /6 s. I order to hotograh a raidly movig subject, the shutter seed is chaged to /8 s. Fid the ew f-umber eeded to maitai satisfactory exosure.

Huygen s Principle: Propagation of Wavefronts. Light Rays and Geometric Optics. The Laws of Reflection

Huygen s Principle: Propagation of Wavefronts. Light Rays and Geometric Optics. The Laws of Reflection Chater 5: Relectio ad Reractio o Light Huge s Pricile: Proagatio o Waverots Ever oit o a waverot roduces wavelets. Radius o each wavelet is vt. New waverot is the surace taget to the wavelets. waverots