ch2-2 thin lens.ppt

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1、3 Thin Lens（薄透镜）（薄透镜）A transparent homogeneous medium bounded by two spherical surfaces is referred to as a spherical lens.If the thickness of such a lens(shown as d in Fig.2-3-1 below)is very shorter than that of object and image distances,and also than radii of curvature of the surfaces,the lens i

2、s referred to as a thin spherical lens.Different types of lenses are shown in Fig.2-3-2.The line joining the centers of curvature of the spherical refracting surfaces is refracted to as the axis of the lens.These interfaces are most frequently spherical segments and are often coated with thin dielec

3、tric films to control their transmission properties.A1 is very close to A2,and both of them can be regarded as one point,this point is defined as the optical center O.QdA A1 1A A2 2C Fig.2-3-1Q1Q3.1 thin-lens equationsReturn to the discussion of refraction at a single spherical interface,Lets locate

4、 the conjugate points for a lens of index nL surrounded by a medium of index n1where the location of the conjugate points S and Sis given by（3-3-1）write on black boardwrite on black board We use equation(3-1)again at the second refracting surface,we have：（3-2）so（3-2）become as：（3-3）（3-1）（）（3-3）we get

5、：(3-4)wherewhereIf we drop the subscripts of S1 and S2 in the equation(3-4),let S denotes object distance and S denotes image distance,(3-4)is rewritten as If the lens is thin enoughQdA A1 1A A2 2（35）shAccordingly,we have the very useful Thin-Lens Equation,This equation often referred to as the lens

6、 makers Formulafrom（31）If s is moved away to infinity,the image distance s becomes the focal length f.（3-63-63-63-6）By using（32），（），（35）can be rewritten as：（3-83-8）Which is the famous Gaussian Lens Formula 高斯公式。高斯公式。for thin lens（3-73-7）The lens which has real focal point（f and f 0）is referred to po

7、sitive lens(正透镜正透镜)，we know from(3-6)that this kind lens requires 1/r1 1/r1 due to 1.The lens which has virtue focal point（f and f 0）is referred to negative lens,this kind lens requires 1/r1 1/r1 due to 0，Q(or F)lies on R-side of H，s（or f)0.In image space:Q(or F)lies on L-side of H,s（or f)0.4.3 rela

8、tion between object and imageWe can get the image by illustration or calculation.和和和和We have the relation from Fig.aboveF F F FQ Q Q QH H H HH H H HF F F FQ Q Q QP P P PP P P Px x x xf f f fs s s sf f f fx x x xs s s sM M M MM M M MR R R RR R R Ry yyyGaussian equationGaussian equationAngular magnifi

9、cationNewtonian Newtonian equationequationlateral lateral magnification magnification Here u and u is the angle between the conjugate light Here u and u is the angle between the conjugate light rays and the optical axis.rays and the optical axis.We can get the result from the figure.Q Q Q QM M M MM

10、M M MH H H HH H H Hu u u u-u-u-u-uQ Q Q Qs s s ss s s sh h h h h h h hThe lateral magnification is in inverse proportion to the angular magnificationFor a single refraction interfaceThis is H.von Helmholtz（亥姆霍兹（亥姆霍兹)equation,in paraxial region tguu,the equation become to Lagrange-Helmholtz equation.

11、nodal point（节点节点）u u u uJ J J Ju u u uJ J J JTo discuss the relation of conjugate line,it is necessary to introduce the concept of nodal pointThe couple of planes whose angular magnification is equal to 1 are called nodal planes.The plane in the object space is called the first nodal plane and the p

12、lane in the image space is called the second nodal plane.The intersection points of the two nodal planes and the axis are called the first nodal and the second nodal point separately,denoted by J and J.nProperties of nodal point:Any incident light ray which passes through the first nodal point J,aft

13、er passing through the system,will pass the second nodal point J parallel to its original direction,as shown in Fig.above.When an optical system is bounded on both sides by air,we have f=f，so When v=1,W=1,so On this condition,J coincides with H and J coincides with H,that is to say,the nodal points

14、coincide with the principal points,as shown in fig.as follow.The optical center of the thin lens is just principle point H and nodal point J.When the index in object and image space is not equal,its nodal point J does not coincide with H.nodal point locates outside of spherical interface.Thin lensFo

15、cal length formula lens makers formulalens makers formulaBrief summaryBrief summaryBrief summaryBrief summary：Image formation equationGaussian formulaNewtonian formula（，）密接透镜组：光焦度密接透镜组：光焦度密接透镜组：光焦度密接透镜组：光焦度 P=1/fP=1/fP=1/fP=1/f，P P P P1 1 1 1=1/f=1/f=1/f=1/f1 1 1 1，P P P P2 2 2 2=1/f=1/f=1/f=1/f2 2

16、2 2，P=PP=PP=PP=P1 1 1 1+P+P+P+P2 2 2 2正负号的法则（共轴球面折射光学系统），具有人规定，设光正负号的法则（共轴球面折射光学系统），具有人规定，设光轴自左向右轴自左向右序序号号物理量符号物理量符号相对位置相对位置正正负负物距物距s物方焦距物方焦距f轴上物点轴上物点Q，物方焦点物方焦点F：在单折射在单折射球面顶点球面顶点A，薄透镜光心薄透镜光心O之左之左之右之右像距像距s像方像方焦距焦距f轴上像点轴上像点Q，像方焦点像方焦点F：在单折在单折射球面顶点射球面顶点A，薄透镜光心薄透镜光心O之右之右之左之左曲率半径曲率半径r 球心球心C在折射球面顶点在折射球面顶点A之右之右之左之左物高物高y像高像高y轴外物点轴外物点P，轴外像点轴外像点P在光轴在光轴之上之上之下之下光线倾角光线倾角u从光轴转向光线从光轴转向光线逆时针逆时针顺时针顺时针牛顿物距牛顿物距x 轴上物点轴上物点Q在物方焦点在物方焦点F之左之左之右之右牛顿像距牛顿像距x轴上像点轴上像点Q在像方焦点在像方焦点F之右之右之左之左The end