Hong Kong Polytechnic UniversityThickLensThickLens:Thick lens is a lens whose thickness along its optical axis cannot be ignored withoutleadingtoseriouserrorsinanalysis.SixCardinalpoints:applicabletoanyopticalsystemfirstandsecondsystemfocalpoints(F,andF2);first and second principal points (H, and H2);firstandsecondnodalpoints(NandN2)Planesnormaltothe axisatthesepoints are called cardinal planesN.H2HPP2PP,NPNP2(a)(b)Optics1----byDr.H.Huang,DepartmentofAppliedPhysics
Hong Kong Polytechnic University Thick Lens: Thick lens is a lens whose thickness along its optical axis cannot be ignored without leading to serious errors in analysis. Six Cardinal points: applicable to any optical system • first and second system focal points (F1 and F2 ); • first and second principal points (H1 and H2 ); • first and second nodal points (N1 and N2 ). Planes normal to the axis at these points are called cardinal planes. Thick Lens Optics 1-by Dr.H.Huang, Department of Applied Physics
HongKongPolytechnicUniversityThickLensBasicEquations:Focal length:1(n -n)(n, n,-n'n,-nTfinR,nR,RR,nn,VNf.Position of principal planes:Wn,-n.Sn,RRn1Distancesdirected,arePosition of nodal points:positive or negative by asignconventionthatmakesnndistancesdirected to then,R,nn,RnleftnegativeanddistancesThick lensformula:to the right, positive.f+f2=1ns;mn'sS。SProperties:Ifn=n',thenr=vands=wH,H, = N,N,H,N, = H,N2FH,= N,F2FH,=N,FOptics1----byDr.H.Huang,DepartmentofApplied Physics
Hong Kong Polytechnic University Basic Equations: Focal length: Position of principal planes: Position of nodal points: Thick lens formula: Properties: If n=n , then r=v and s=w ( )( ) 1 2 1 1 2 1 R R t nn n n n n nR n n nR n n f L L L L L − − − − − − = 2 1 f n n f = − f t n R n n r L L 1 2 − = f t n R n n s L L 2 1 − = − 1 2 1 t f n R n n n n v L L − + = − 2 1 1 t f n R n n n n w L L − − = − 1 1 2 + = o i s f s f o i n s ns m = Distances are directed, positive or negative by a sign convention that makes distances directed to the left negative and distances to the right, positive. Thick Lens 1 1 2 2 2 2 1 1 1 2 1 2 1 1 2 2 F H N F F H N F H H N N H N H N = = = = Optics 1-by Dr.H.Huang, Department of Applied Physics
HongKongPolytechnicUniversityThickLensExample: Determine the focal lengths and the principal points for a 4-cm thick, biconvexlenswithrefractive indexof 1.52and radi of curvature of25 cm,whenthelens capstheend of a long cylinder filled with water (n=-1.33).Solution: n,=1.52, n=-1,n'=1.33, t=4 cm.Thefirstrefractionsurfaceisaconvexplane,soR,=25cmThe second one is a concave plane, so Rz=-25cm. According to equation1ni-n' ni-n (n,-n)(ny-n) tfinR2nR,RR2nnwe can get f=-35.74cm to the left of the first principal plane. Fromnnwe havef2=47.53cm to the right of the second principal plane.Equationsn,niS:n,R2n,R,give us r=0.715cm and s=-2.60cmOptics1----byDr.H.Huang,DepartmentofAppliedPhysics
Hong Kong Polytechnic University Example: Determine the focal lengths and the principal points for a 4-cm thick, biconvex lens with refractive index of 1.52 and radii of curvature of 25 cm, when the lens caps the end of a long cylinder filled with water (n=1.33). Solution: nL=1.52, n=1, n=1.33, t=4 cm, The first refraction surface is a convex plane, so R1=25cm. The second one is a concave plane, so R2=−25cm. According to equation we can get f1=−35.74cmto the left of the first principal plane. From we have f2=47.53cm to the right of the second principal plane. Equations give us r=0.715cm and s=−2.60cm. ( )( ) 1 2 1 1 2 1 R R t nn n n n n nR n n nR n n f L L L L L − − − − − − = 2 1 f n n f = − f t n R n n r L L 1 2 − = f t n R n n s L L 2 1 − = − Thick Lens Optics 1-by Dr.H.Huang, Department of Applied Physics
HongKongPolytechnicUniversityThickLensExample: (a)Find the cardinal points and sketch a ray diagram for the hemispherical glasslensshowninthefigure.Theradiiof curvatureareR,-=3cmandR,=oo,andthelens inairhasa refractive index of 1.50. (b) Sketcha ray diagram to locate the image of a1-cm tall object3cmtotheleftofthefirstprincipalpointforthislensSolution: (a) n,=1.50, n=n'=1, t=3 cm11n,-n'n,-n (n,-n)(n,-n) tfi =-6 cmf =6cm6f.nR,nR,R,R2nnyn,-n'51=0n,R21ni-nt =-2 cmS:n,R,3NNv=0 cm andw=-2cmH,F2VIROFH2(b) s。=-3 cm,s=-6 cmf+f2=1Air3nz=1.50s。SiAir1cm+ns,2m=3cmn'sOptics1----byDr.H.Huang,DepartmentofAppliedPhysics
Hong Kong Polytechnic University Thick Lens Example: (a) Find the cardinal points and sketch a ray diagram for the hemispherical glass lens shown in the figure. The radii of curvature are R1=3 cm and R2=, and the lens in air has a refractive index of 1.50. (b) Sketch a ray diagram to locate the image of a 1-cm tall object 3 cm to the left of the first principal point for this lens. Solution: (a) nL=1.50, n=n=1, t=3 cm v= 0 cm and w=−2 cm (b) so=−3 cm, si=−6 cm 1 1 2 + = o i s f s f ( )( ) 6 cm 6 cm 6 1 1 1 2 1 2 1 1 2 = − = − = − − − − − − = f f R R t nn n n n n nR n n nR n n f L L L L L 2 2 cm 1 = − − = − f t n R n n s L L = 2 = o i n s ns m 0 1 2 = − = f t n R n n r L L Optics 1-by Dr.H.Huang, Department of Applied Physics
HongKongPolytechnicUniversityThickLensExample: Find the cardinal points and sketch a ray diagram for the thick lens shown in thefigure.The radii of curvature are R,=-10 cm and R,=25 cm and its thickness on axis is 5 cm.Thelens is situated inair andhas a refractiveindexof1.60Solution: n,=1.60. n=n'=1. t=5 cm8.851n, -n'n,-n.(n, -n)(n, -n)tf =11.3 cmf, =-11.3 cmJ100nR,nR,R,R,nni1.6-1n,-n'<11.3×5=0.847cmv=r=0.847cmn,R21.6×251.6-nn11.3)x5 = -2.12 cmw= s = -2.12 cmS:n,R1.6(-10123VIFRONHN2H2F2-3In, =1.6AirAir1PP,PP2Optics1----byDr.H.Huang,DepartmentofAppliedPhysics
Hong Kong Polytechnic University Thick Lens Example: Find the cardinal points and sketch a ray diagram for the thick lens shown in the figure. The radii of curvature are R1=−10 cm and R2=25 cm and its thickness on axis is 5 cm. The lens is situated in air and has a refractive index of 1.60. Solution: nL=1.60, n=n=1, t=5 cm ( )( ) 11.3 cm 11.3 cm 100 1 8.85 1 2 1 2 1 1 2 = = = − − − − − − − = f f R R t nn n n n n nR n n nR n n f L L L L L 11.3 5 0.847 cm 0.847 cm 1.6 25 1.6 1 1 2 = = = − = − = f t v r n R n n r L L ( ) ( 11.3) 5 2.12 cm 2.12 cm 1.6 10 1.6 1 2 1 − = − = = − − − = − − = − f t w s n R n n s L L Optics 1-by Dr.H.Huang, Department of Applied Physics