Massachusetts Institute of Technology 2.71/2.710 Optics Spring 2014 Solution for HW2

Transcription

1 Mdiied rm Pedrtti 8-9 a) The schematic the system is given belw b) Using matrix methd rm pint A t B, A B M 2lens D 0 0 d d d 0 d d Frm the abve matrix, we see that A and D are unitless, B is in the unit length, and has the unit /length The eective cal length and lcatin the principle planes can be calculated rm Table 8-2 Pedrtti: EFL : eq 20 cm, FFP : p D 30 cm, BFP : q A 0 cm, PP ( ) ( ) : r D 0 cm, PP2: s A 0 cm Here, PP represents the lcatin the starting plane the system with respect t the riginal rntal plane A PP2 represents the lcatin the mdiied ending plane the system with respect t the riginal ending plane B

2 c) An example is sketched with the bject placed at 20cm t the let the irst lens The bject is lcated 0cm let t PP Frm the lens law, we get: 200, si 20 cm 0 s 20 0 i We ind that the image is lcated 20cm let t the 2 nd principal plane, which is 25cm let t L 2

3 2 Plan-cnvex dublet lens In the visible spectrum, the reractive index glass is clse t a cnstant as shwn belw in the spectrum prvided by Newprt a) Using the matrix methd t calculate the verall ptical respnse, we can get M M M M M M ttal R3 t2 R2 t R t2 t n2 n 0 n2 n n2 n n0 n n0 0 0 R3 n 0 R2 n 2 R2 n A B D and the ptical pwer the cmpsite lens can be calculated rm the equivalent cal length P eq 00095mm b) I a plane wave is incident rm the let, it cuses n the BFP A BFP 097mm Therere the plane wave cuses 02mm ater the right surace the lens 3

4 3 A Telepht Lens a) The cal length each individual lens can be determined as the llwing The ABD matrix r tw thin lens is: M 2lens 0 0 d d d 0 d d Frm the matrix we can set the llwing parameters t be: EFL : eq 300 m, BFL : q A 00 mm Plugging in the tw values and using d=20mm, we get 80 mm, 50 mm 2 b) the principal planes can be btained rm: M 2lens 20 3 A B 9 D n D 0 n PP 240 mm, PP ( A) mm 4

5 PP is 240mm let L and PP2 is 200mm let L2 c) The entrance pupil is identical t the aperture stp The diameter can be btained rm the equatin r F- number: N 4, D 300mm 75 mm D N 4 d) The mst eicient way t predict the answer is t graphically think abut hw much light prpagates with the given angle variatin We can cnvert the input angle int utput vertical distance by recgnizing that the eective distance prpagatin until the cus is EFL: xapprx EFL tan( ) EFL 03mm Is it really true? Let s check mathematically with the rigrus matrix methd We can cnstruct a new system matrix that includes the prpagatin t the BFP: xut BFL A B xin 0 B D BFL xin ut 0 D, in D in since BFL=-A/ This can be urther simpliied by: A B D BFL B D B ( B) EFL Indeed! Here, AD B cmes rm the act that the determinant the system matrix is equal t the rati between the initial and inal reractive indices, n / 0 n Therere the distance between the tw cuses is 03mm 5

6 4 Mdiied rm Pedrtti 3-5 Amng elements A, L, and L2, the ne whse image thrugh the elements t its let subtends the smallest angle at the center the EnP is the ield stp Aperture A in this case is ur entrance pupil The rim A at the EnP subtends 90 The rim L at the EnP subtends tan (3 / 3) 45 L2 shuld be imaged twards the let, thrugh L This iamge, labeled L2, can be calculated as:, si 2 cm ; s 4 6 i si yi M 3, yi 9 cm s 3 Therere, the rim L2 at the EnP subtends tan (9 /5) 3, which is the smallest angle, making L2 the ield stp the system, and L2 the EnW b) The EnW is the image the FS thrugh the ptical cmpnents t its let In a) we calculated this t be L2 The ExW is the image the FS thrugh the ptical cmpnents t its right Since there are n cmpnents t the right, the ExW is the L2 itsel c) The schematic the system is given belw The marginal rays in this illustratin start rm P and tucnes the edges the EnP Ater hitting L, they aim tward P, and ater hitting L2, they are redirected twards P, which is the inal image (Image redit: 2007 Pearsn Prentice Hall, Inc) Pearsn Prentice Hall All rights reserved This cntent is excluded rm ur reative mmns license Fr mre inrmatin, see 6

7 5 amera lens and Image Stabilizer system a) ( n ) (05) R R mm The transer matrix rm A t A can be und as: 0 s s ( d s)( s ) s d s A B 0 0 d s D The distance is d=36nm The imaging cnditin is B=0, which can be slved r s t yield ( s 30)(s 6) 0 Which is the crrect answer? T have a demagniied image (s<d-s), the valid answer is s=6cm b) Ater the rtatin the camera, x ( d s)sin 524mm Then we mve the lens up by distance : x x, x, i xi s x d s Therere the lens must be mved by 0873mm upward t cmpensate r the shaking Surce unknwn All rights reserved This cntent is excluded rm ur reative mmns license Fr mre inrmatin, see 7

8 MIT OpenurseWare 27 / 270 Optics Spring 204 Fr inrmatin abut citing these materials r ur Terms Use, visit: