Sphericl refrctig urfce Here, the outgoig ry re o the oppoite ide of the urfce from the Icomig ry. The oject i t P. Icomig ry PB d PV form imge t P. All prxil ry from P which trike the phericl urfce will iterect t P. Fig. 34.2 C i o the ide of the outgoig ry, d o the rdiu of curvture i poitive. Similrily, P i rel imge poit (o the ide of the outgoig ry), d o the imge ditce i poitive. θ = α+ φ From trigoometry, d φ = β+ θ R Sell lw i i θ = iθ, or θ = θ PHYS 53 08W
h tα = α + δ h tβ = β δ h h h tφ = φ R δ h R Comiig thee equtio to elimite the gle d, + = (phericl refrctig urfce) R The lterl mgifictio of exteded oject i m= y y Fig. 34.22 PHYS 53 08W 2 h
y tθ = iθ y tθ = iθ iθ Ad uig Sell lw iθ = Hece m = Appret depth of pool y y = Here i refrctig urfce with R= + = 0 w ir = wter PHYS 53 08W 3
= = I thi ce, ice the ource i i the wter, d w w + = 0 = w = ir Thi lee Lemker equtio The phericl refrctig urfce lyi w doe uig thick le. Imgie the thicke of the thick le Fig. 34.33 hrikig to very mll vlue to ecome thi le. The imge for the firt ide ow ecome the oject 2 for the ecod ide. So the oject d imge ditce for the firt urfce re d Thoe for the ecod urfce re d 2 2 PHYS 53 08W 4
Sice i o the oppoite ide of the icomig ry, 2 = 2 For the firt urfce, efore, For the ecod urfce, But = = = c + = R + = c c 2 2 R2 (the d c ide re i ir) d we et 2 = =, the idex of refrctio of the le, d With thee utitutio i the ove two equtio, we dd them d oti + = ( )( R 2 R2 ) PHYS 53 08W 5
Normlly we me the oject ditce d the imge ditce Thu + = ( )( ) (thi le) R R 2 A with the mirror, whe the oject i t ifiity for covex or covergig le, the icomig ry re prllel, d the le will rig the ry to focu. Whe the oject i t focl poit, the outgoig ry will e prllel, d the imge will e formed t ifiity. The focl legth f i the ditce from the le to either focl poit F, or F 2. Thu if the icomig ry re prllel, The d. = = f Fig. 34.28 PHYS 53 08W 6
f = ( )( ) R R 2 (lemker equtio for thi le) d + = (thi le) f f I poitive for covergig le. For cocve or divergig le, icomig prllel ry pper to diverge from F 2. Thee ry c lo e revered. Icomig ry tht re heded for F, will emerge prllel. f i egtive for divergig le. Fig. 34.3 PHYS 53 08W 7
Fig. 34.32 Note the differet type of covergig (thicker i the middle th t the edge) lee, d divergig (thier i the middle th t the edge) lee. The formule tht we developed pply to ll thee lee. Rememer the ig covetio. I thi figure (covergig le),,, R re ll poitive. R i egtive. ( d 2 R R 2 re ot how. See Fig. 34.35). Fig. 34.29 PHYS 53 08W 8
The mgifictio for thi le c e otied from the previou figure. Uig imilr trigle, m = Grphicl method for lee Three well defied ry defie the poitio of exteded imge. Oly two re eeded. Fig. 34.36 For the covergig le, the imge i rel, d iverted (i thi ce). The oject ditce, Imge ditce, d focl legth re poitive. Wht out the rdii of curvture? PHYS 53 08W 9
Prolem 34.32 A covergig le with focl legth of 2.0 cm form virtul imge 8.00 mm tll, 7.0 cm to the right of the le. Determie the poitio d ize of the oject. I the imge erect or iverted? Are the oject d imge o the me ide or oppoite ide of the le? Drw pricipl ry digrm for thi itutio. PHYS 53 08W 0
For the divergig le, the imge i virtul d erect (i thi ce). The oject ditce i poitive, d the imge ditce d focl legth re egtive. Covex le exmple. PHYS 53 08W
Some pplictio. The imple mgifier Fig. 34.5 The cloer oject i to the uided eye, the lrger will e the gle θ d hece gulr ize. Thi will reult i lrger retil imge. However, the cloet poit to the eye o which the eye c properly focu i the er poit. Thi i out 25 cm for the verge youg pero. A wy to mke the gulr ize lrger i to ue imple mgifier. If virtul imge i formed, the imge will e erect d c e very lrge. PHYS 53 08W 2
The imge i comfortle to view whe t ifiity, o the oject mut e plced At the focl poit F of the mgifier. y θ f 25cm The gulr mgifictio M = = = θ y f 25cm (rememer m i the lterl mgifictio) The vlue of M chieved re out 3 x to 4 x. 2. The refrctig telecope The refrctig telecope h two covergig lee. My mll telecope ued t home re refrctor. All ig reerch telecope re reflector. PHYS 53 08W 3
Telecope view oject which re very ditt d o the icomig ry re Eetilly prllel. The firt imge I i formed t the focl poit of the Ojective le, F 2. The focl poit of the eyepiece F i t the me loctio So tht the imge formed y the eyepiece i t ifiity. I The ditce etwee the ojective le d the eyepiece le i the f + f 2 The gulr mgifictio, efore, i M y f y f θ 2 = = = (telecope) θ f f 2 PHYS 53 08W 4
Prolem 34.99 Whe oject i plced t the proper ditce to the left of covergig le, the imge i focued o cree 30.0 cm to the right of the le. A divergig le i ow plced 5.0 cm to the right of the covergig le, d it i foud tht the cree mut e moved 9.2 cm frther to the right to oti hrp imge. Wht i the focl legth of the divergig le? PHYS 53 08W 5
Prolem 34.04 A oject i plced 8.0 cm from cree. () At wht two poit etwee oject d cree c covergig le with 3.00 cm focl legth e plced to oti imge o the cree? () Wht i the mgifictio of the imge for ech poitio of the le? PHYS 53 08W 6