Reminder, repetitin Image frmatin by simple curved surface (sphere with radius r): sin sin n n The pwer (refractive strength): n n n n i r D Applicatin: fr the human eye e.g. the pwer f crnea medium r mm n n -n D dpt air 0,37 48 crnea 7,7,37 *** Image frmatin by tw curved surfaces (radii r ; r ) (thin lens apprximatin): Lens equatin and lens-makers equatin: i f ( n, ) r r
Image frmatin by lenses Simple magnifier We have t cmpare tw cases: eye lks at the O bject. withut lens frm the cnventinal near pint (a 5 cm), under the angle f. with lens frm the distance, under the angle f I virtual image Angular magnificatin: N tan tan and we use f i
In the case f simple magnifier: O tan N tan O a Tw pssible answers: I. if i = a than II. if i = than a a f i a N +, f a N f In the I. case eye lks at the virtual image with accmmdatin, in the II. case withut accmmdatin, eye is fcused at infinity, thus = f. *** Lens systems () micrscpe Withut accmmdatin, eye is fcused at infinity. Angular magnificatin f micrscpe: N tan tan da f f 3
Lens systems () pwer (refractive strength) Hw high the cllective fcal length f tw clse juxtapsed lenses is L (f ), L (f )? Let s apply the lens equatin fr O as a virtual bject. Dcll. D D f f f f f f cllective cll. In such cases pwers are added. Units [/m], diptre, [dpt]. Applicatin e.g.: glasses, cntact lenses. *** There are phenmena that cannt be explained by this mdel. 4
Interference (tw r mre waves meet) the mst imprtant phenmenn in cnnectin with waves E.g. water wave : it can be bserved directly. Because it changes slwly enugh (lw frequency, f ) and the typical (wave) size is large enugh (lng wavelength, ). Light waves are different. Micrscpic (shrt wavelength, λ); quick change (high frequency, f ) At certain cnditins patterns can be frmed, which dn t change in time, and their size is much larger than the wavelength,. Incherent and cherent waves Rise f cherent waves is cntrlled in space and time, they are synchrnized smehw. 5
Physical r wave ptics (ther mdel) Its bases: HuygensFresnel-principle Accrding t the Huygens principle, elementary waves riginate frm every pint f a wavefrnt, and the new wavefrnt is the cmmn envelpe f these elementary waves. The laws f rectilinear prpagatin, the reflectin and refractin can be described by this mdel as well. Fresnel supplemented this by bserving that the superpsitin principle is als in effect during the frmatin f the new wave frnt, which is nthing else than the quantitative frmulatin f the empirical fact that waves will prpagate thrugh each ther withut disturbance. Typical experiment and pattern f light interference Yung s duble slit experiment (diffractin) The places f cnstructive and destructive interference are determined by the difference in phase (). 6
At a certain place the vibratinal states are demnstrated by rtating vectrs: The amplitude f the net vibratin (A resultant ) is given by the vectr sum f the cmpnents (A). Our eyes are sensitive t the light-pwer (P), that is prprtinal t the square f the amplitude. Thus A resultant P res., and A res. = A + A hence P res. P + P. Resultant (A resultant ) f tw vectrs (A, A ), r the square f it, if the angle between them is : P A resultant = A + A A A cs(- ) (csine therem) P A resultant = A + A + A A cs If A = A = A, than A resultant = A ( + cs) 7
The difference in phase () is determined by the relatin f difference in path length (s) and the wavelength (). If L >> d, the difference in path length s = dsin. The difference in phase is given as: s d sin d tan d x L Demnstratin: Maxima can be bserved at places crrespnd t = k r s = k; k = 0,,, cnditin. Applicatins: determinatin f the reslving pwer f micrscpes, 8
Light is electrmagnetic wave thus can be plarized transversal linearly plarized light r plane plarized light But elliptically plarized light als exists. Optical anistrpy E.g. in an anistrpic matter the speed f a suitably linearly plarized light depends n the directin f prpagatin. The reasn f it is cnnected t the structure f matter. Cnsequences, applicatins: duble refractin, plarizatin micrscpe 9