光学光学光学光学 (4).pdf
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1、-95-Chapter 4 Geometric Optics(Zhaos Chap I,4,5,6,7,9.;Hechts.5.1-5.4;6.1,6.2)(1)Why is it called geometric?The problems can be solved geometrically,at most by analytical geometry(such as the matrix method of ray tracing).(2)Why it can be solved geometrically?Treat the light as0.This means there is
2、no concern of wave characters of light,such as interference,diffraction,etc.We shall treat light as“rays”traveling in straight lines(the wavelength of light is negligible compared to the dimension of the problem in concern).The“ray”is a line representing the energy flow of the light wave and in isot
3、ropic media,it is same as direction of wave vector k.(3)Why Bother?G.O.though lacks of scientific(from theoretical point of view)significance,it is still having probably the broadest applications in technology development in optics (4)What can we do with G.O Modify the incident wavefront -96-Example
4、:Change the wave front and Image formation:In experiments in physics,there are numerous occasions that we need to detect the light emitting or scattered from an object,not even considering that our own eyes are a pair of complicated lens(or camera)system.The most common set up would be:We need to me
5、asure or record(a)Intensity such as molecular spectroscopy(b)Image For purpose(a),we need to collect as much light as possible.For purpose(b),we need a device to convert every point of the object into -97-every single point of the image,while keeping the proportion(one to one correspondence without
6、distortion).In sections below,we are going to study what are these devices,why they work and what are their limitations.4-1 Jargons in geometric optic Focal points,concave,convex,real,virtual images,objects,object-Image conjugates Take examples that we are already familiar with,a)convex lens light p
7、asses through a convex lens will be more converged Optical axis:The line passes the center of the lens and -98-perpendicular to it.of:a special point on the optical axis;lights from of after optical elements will be parallel beams.Or of has image at(infinity).if:another special point on optical axis
8、;beams parallel to the optical axis after pass optical element will focus toif.Or object at will have its image atif.b)concave lens:Light passes through a concave lens will be more diverged.The of is a virtual object on the optical axis whose image is at infinity;ifis the virtual image whose corresp
9、onding object is at infinity.-99-1)Real,Virtual Object:In case(C),(D),object AB are real objects for1L.Real means for the optical elements(such as1L),the incoming lights from the object are diverging.In case(C),if we insert a second lens into the system(2L),at the axial location as shown,A B(the rea
10、l image of AB through1L)now becomes a virtual object for2L,the incoming light to the 2L(another saying is that 2Lsees the incoming light)are converging.In case(D),A B(the virtual image of AB through1L)is a real object for2L.2)Real,Virtual Image A B is a real image in case(c)formed by1L,the lights th
11、at form the image are converging.The real image can be projected on a real screen.-100-A B in case(D)is a virtual image by1L,the lights“forming”it are diverging.If the objective points and image points have a 1 to 1 relation(i.e.each objective point corresponds to one and the only one image point),i
12、t means all the light from the object after passing through the optical element(lens here)will converge to its image point(for the real image case;or diverge to virtual image point).The corresponding objective and image points are called conjugate points.In(C),(D):1LAA 1LBB They are conjugate points
13、 by 1L 4-2 Fermats Principle The OPL for all light rays between conjugate points are equal.It is fairly easy to prove for real object and real image ease.The light rays connecting the object point O and image point I through the optical element have to be stationary.The OPL of these different rays c
14、annot be -101-maximum or minimum,have to be a constant.For virtual object or image,their OPL have to be counted as negative(try proving this as an exercise,hint:set up using extra lens to make virtual image as object again and forming real image with second lens),and the refractive index n in OPL=nl
15、,has to be taken corresponding to the objective or image side respectively.So if any interface can satisfy the constant OPL between pointsQ andQ,they will be a pair of Object Image conjugate with respect to that interface.Such interface can be derived by requiring:(Hechts 5.2.1,Zhaos 4.4)QMMQconstQM
16、MQconst+=contour of point M for real or virtual image(object)The contour of M,satisfying the above equation is generally an aspheric curve(or surface,such as elliptical,hyperbolic).These aspheric optical elements are more difficult to manufacture in great precision than spherical ones.Since spherica
17、l optical elements are widely used and easier to make,we are going to study in detail of such optical lenses or mirrors,to see -102-under what condition that the spherical ones can be treated as ideal.Ideal optical Element:(1)All light rays from one point source can be transformed into another point
18、.11 relation between image and object,so to the lines and planes.(2)The optical element can cover wide range of objective distance,not only for a specific pair of object image points.(3)No distortion,i.e.keep the original shape of the object,a constant magnification value in image plane.4-3 Refracti
19、on at a Single Spherical Surface (Fig 5.6 Hechts or Fig 5.1 Zhaos)We need to find relation betweenoS,iS.If it is independent of (orh,1i,2i)then all rays coming from Q can be converged intoQ,i.e.Q,Q -103-are conjugate.The position of the image is most generally in a functional form:0012(,.)iiSF S n n
20、 ri i=.Of course,not all the variables are independent,they are related by Snells law,triangular relations etc.Neglect the detail derivation(refer to Hechts 5.2.2),we get:22202222220000114 sin()()2()()iiiiiSSrnSrnSrnSrnSr=+(4-1)Generally,0S and iS are dependent on(that is where the ray hit the surfa
21、ce),so rays from 0S of different angle generally interact the axis at different distance,except for a special pair0S,iS where 22022220022000()()110()()iiiiiSSnSrnSrnSrnSr=+=+Such0S,iS defines the location of Stigmatic Points for the spherical surface(these special pair can achieve so called broad be
22、am image formation.i.e.all light from the object at O are converged to the image point I).So(4-1)shows that the spherical surface is not an ideal optical element except for a special pair of points.4-4 Paraxial Approximation.Under paraxial condition for points on the axis,i.e.-104-220hS,2iS,2r or 2,
23、2,21 Then 22sin022 in(4-1)2202222000()()iiiSSnSrSrn=+(4-2)000()()iiiSSn SrSrn=+000iiin rnrnnSS+=000iiinnnnSSr+=(4-3)For image focal point,if:0S ,iiSf 0iiinnnfr=0iiinrfnn=(4-4)Similarly for object focal point:iS ,00Sf 000in rfnn=(4-5)(4-3)object-image relation can be rewritten in the more familiar fo
24、rmula(Gausss formula):-105-001iiffSS+=(4-6)Under paraxial condition,that each point on the axis0S,will form an image at iS on the axis based on(4-6)*Sign convention for spherical refraction and thin lenses(Light entering the lens from Left side)0S,0f +left of vertex A iS,if +right of A R +c is right
25、 of A 0y,iy +above the optical axis ox +left of 0f(x is used in Newton formular)ix +right of if +optical axis to ray is counter clock wise.Choose the convention and stick to it,then from the computation to determine the positions of the image relative to the optical elements.This is the basics of ge
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