EE 119 Homework 6 Solution

Transcription

1 EE 9 Hmwrk 6 Slutin Prr: J Bkr TA: Xi Lu Slutin: (a) Th angular magniicatin a tlcp i m / th cal lngth th bjctiv ln i m cm (b) Th clar aprtur th xit pupil i 35 mm Th ditanc btwn th bjctiv ln and th ypic i d + 84cm Th magniicatin at uch a ditanc i m /( + d) /( + ) / / 45 S th xit pupil i 45 tim mallr than th bjctiv ln, maning that th bjctiv ln ha a diamtr 35 x mm (c) Th bjct ild angl i th angl ubtndd by th chi ray that barly tuch th utid th ypic ln S it i givn by tan d θ θ 034 (d) Th bjct and imag ild angl ar rlatd t ach thr by th angular magniicatin, th imag ild angl i θ 4 () Th diractin limitd angl i dtrmind by diractin at th ntranc pupil, which i th bjctiv ln It ha a diamtr 575cm 0575 m λ 55 0 θ inθ D Th imag angl that thi crrpnd t i 45 θ mrad Thi i mallr than th rlutin th y, th limit rlutin n th tlcp i th y, nt diractin Or Th maximum magniicatin th tlcp r it nt bing diractin limitd atii that CA 575 / > 45 max Thrr, th limit rlutin n th tlcp i nt diractin, but th brvr y

2 () Sinc th limit n th rlutin th micrcp i th brvr y, thrugh th tlcp, n can rlv bjct paratd by an angl α 03mrad / / mrad S th minimum ditanc in mtr btwn th Eminnt Britih Captain and th mytriu black-laggd hip ptntial dm i 4 D 0/ α 0/ m 5km Slutin: A thi i a dign prblm, thr i n xact anwr Th llwing paramtr huld b includd in yur anwr, and th grading i bad n thm: () agniicatin; () Chic CA and CA ; (3) Diagram with ray trac, ntranc and xit pupil; (4) Chic and I yur dign lw i ranabl, yu ll gt ull crdit A ampl dign chm: Th tlcp mut b abl t rlv a atur that i 74500mil/0 7450mil wid and mil away, which crrpnd t an angl θ /(746 0 ) Th magniicatin that wuld b rquird r th cn th y t rlv thi i rad T mak ur th tlcp i nt diractin limitd, > CA r max CA CA 60 (*) Sinc th iri th y i 4mm, th iz th xit pupil huld match, r lightly largr than that, i CA ~ 4mm Frm lutin prb (b), w knw that th tranvr magniicatin th bjctiv ln (ntranc pupil) and it imag (xit pupil) thrugh th ypic i m / / 30 Th diamtr th bjctiv ln mut b at lat Plugging thi valu mm cm CA cm 4 8inch int th rlutin critrin Eq(*), w that 55 CA i valid S with thi chic, CA and CA, th 60

3 tlcp i nt diractin-limitd Nw w nd t ch and Th tw numbr can b any, but lt ch th with ranabl argumnt Th bjct ild angl θ i dtrmind by th iz th ypic Lt ch 5cm th iz th ypic t b 3cm, thn θ tan ( ) Th imag illd angl θ ' i imply rlatd tθ by magniicatin W al knw that 60cm and 6cm I 6cm, thn w hav 5cm θ tan ( ) 0 048rad 6 and th imag ild angl θ ' 44rad Al m, hnc ' 067 cm ' + and m 30 Lt ch cm, thn Fr ummary, 30, CA cm 4 8inch, CA ~ 4mm cm, 60cm, 6cm, ' 067cm ypic iz 3cm 3 Slutin: W want t i th wrking ditanc r thi micrcp i largr than mm I that i th ca, thn w can put th gla lid btwn th micrcp bjctiv and th ampl t b xamind 3

4 Givn 0, 5cm and x' 60mm, w knw that tt 5cm 5, 4 A x', 4cm Uing Ln law t ind, w hav + > Hnc -5cm > > mm + x' + S it i pibl t u thi micrcp t lk at a ampl undrnath a gla lid thickn mm 4 Slutin: (Thr can b many anwr, a lng a yu clarly pciy lctin magniicatin; cal lngth and diamtr th bjctiv; cal lngth th ypic, and ray trac th ytm, yu ll gt ull crdit) 4

5 Th y can rlv an bjct iz ~008mm 80 μm at th ditanc 5 cm T hav a rlutin μm, th ttal magniicatin th micrcp i 80μm tt μ m 80 Pick a cmmn 0x bjctiv, thn th ypic huld hav th magniicatin x' 6cm Sinc th tandard tub lngth i 6cm, rm 0, w gt th cal lngth th bjctiv ln t b 0 8cm 8mm Al, 0 > 84mm > 5mm (wrking ditanc) Sinc 5cm (5 cm i th tandard viwing ditanc; nar pint), 5cm 6 5cm 4 Th ditanc btwn th bjctiv ln and th ypic i thn d + x' cm In rdr r th micrcp t b nt diractin-limitd, max 40NA Fr 80, NA 0 33 Lt ch NA 0 4 CA / n, θ 0 4 Thu CA mm Summary: tt 80; bjctiv 8mm, 0, NA 0 4 ( CA 6 7mm ) ypic 6 5mm, 4 x' 6cm, 84mm 5mm wrking ditanc d 3 05cm > 5

6 I th bjct id wr immrd in il (n5), 84 ' 5 6mm > 5mm n 5 Fr CA 67mm, θ CA ' / CA / NA ninθ ' nθ ' n( ) 09 / n CA / / n That man w can rlv mallr atur iz with th am dign Th magniicatin will incra by 5, which ar ' 68cm ' 056cm and tt ' Fr th micrcp nt t b diractin-limitd, max 40NA > NA 0 5 Thrr, with th abv dign, th wrking ditanc bcm 56mm whn th bjctiv i immrd in il n 5 Thi till mt th rquirmnt > 5mm Al, NA incra, micrcp ha bttr rlutin and it i nt diractin limitd tt incra t, which man that can b mad largr ( can b mallr) 5 Slutin: (a) 6

7 (b) Th ditanc btwn th lid and th prjctr ln i in th diagram p 0 A m 00 d + d + 0 p d 0 cm (c) Th ditanc btwn th prjctr ln and th crn i d d A m 00, d 00 d 0 m d (d) Th ditanc btwn th ilamnt and th cndnr i in th diagram By Ln law, w hav + > 0 + Slving r, w gt 8 54cm 6 7