1 1 1 f R1 R s s f. SPH3UW Unit 7.6 Convex Lenses Page 1 of 9. Notes. Properties of a Converging Lens

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1 SPH3UW Unt 7.6 Cnvex Lene Page 1 9 Nte Phyc Tl bx Thn Len an ptcal ytem wth tw reractng urace. The mt mplet thn len cntan tw phercal urace that are cle enugh tgether that we can neglect the dtance between them. Cnvergng Len a len that ha the ray cnverge t a ngle pnt, uch a a duble cnvex len. Dvergng Len a len that ha parallel ray dverge, thu gvng the len a negatve value, uch a a duble cncave len R1 R2 y m y Len Maker Equatn n 1 Object-Image Relatn - Lateral Magncatn:. Prperte a Cnvergng Len The prperte a duble cnvex len (called a cnvergng len) allw a beam parallel ray that pa thrugh the len t reract t a pnt called the cu, (we ay that the ray cnverge t a pnt). Smlarly ray that leave the cu and pa thrugh a cnvergng len emerge a a beam parallel ray. A wth a cncave mrrr, a cnvergng len can r an mage an bject. Ung the ame gn rule a we dd wth the cncave mrrr we determne a relatnhp between the bject dtance, and the bject mage, and the cal length the len,. Th equatn knwn a the bject-mage relatnhp and dentcal t the relatnhp we created when ung the mrrr.

2 SPH3UW Unt 7.6 Cnvex Lene Page 2 9 Frm the abve dagram y y y y The rean r the negatve gn that the mage belw the ptc ax and y negatve. Becaue the trangle OAF 2 and P Q F 2 are mlar: y y y y Cmbnng, th gve u: 1 1 1, the requred relatnhp y Al we btan, m the lateral magncatn rmula. y Radu Curvature

3 SPH3UW Unt 7.6 Cnvex Lene Page 3 9 Step-by-Step Methd r Drawng Ray Dagram The methd drawng ray dagram r duble cnvex len decrbed belw. The decrptn appled t the tak drawng a ray dagram r an bject lcated beynd the 2F pnt a duble cnvex len. 1. Pck a pnt n the tp the bject and draw three ncdent ray travelng tward the len. Ung a traght edge, accurately draw ne ray that t pae exactly thrugh the cal pnt n the way t the len. Draw the ecnd ray uch that t travel exactly parallel t the prncpal ax. Draw the thrd ncdent ray uch that t travel drectly t the exact centre the len. Place arrwhead upn the ray t ndcate ther drectn travel. 2. Once thee ncdent ray trke the len, reract them accrdng t the three rule reractn r cnvergng lene. The ray that pae thrugh the cal pnt n the way t the len wll reract and travel parallel t the prncpal ax. Ue a traght edge t accurately draw t path. The ray whch traveled parallel t the prncpal ax n the way t the len wll reract and travel thrugh the cal pnt. And the ray whch traveled t the exact centre the len wll cntnue n the ame drectn. Place arrwhead upn the ray t ndcate ther drectn travel. Extend the ray pat ther pnt nterectn. 3. Mark the mage the tp the bject. The mage pnt the tp the bject the pnt where the three reracted ray nterect. All three ray huld nterect at exactly the ame pnt. Th pnt merely the pnt where all lght rm the tp the bject wuld nterect upn reractng thrugh the len. O cure, the ret the bject ha an mage a well and t can be und by applyng the ame three tep t anther chen pnt. 4. Repeat the prce r the bttm the bject.

4 SPH3UW Unt 7.6 Cnvex Lene Page 4 9 One gal a ray dagram t determne the lcatn, ze, rentatn, and type mage whch rmed by the duble cnvex len. Typcally, th requre determnng where the mage the upper and lwer extreme the bject lcated and then tracng the entre mage. Ater cmpletng the rt three tep, nly the mage lcatn the tp extreme the bject ha been und. Thu, the prce mut be repeated r the pnt n the bttm the bject. I the bttm the bject le upn the prncpal ax (a t de n th example), then the mage th pnt wll al le upn the prncpal ax and be the ame dtance rm the mrrr a the mage the tp the bject. At th pnt the entre mage can be lled n. Image lcatn r cnvex len When the bject lcated n rnt and utde the cal pnt a cnvergng (cnvex) len, then the mage real, nverted, and n the back de the len. When the bject lcated between the cal pnt and the cnvergng len, then the mage vrtual, uprght, larger than the bject, and n the rnt de the len. The llwng et dagram llutrate the mage lcatn (n red) a the bject (n blue) mve tward the cnvex len. The lat dagram repreent a vrtual bject, n th cae yu can apply the Burn-Schlueter Therem (BST) and treat the cnvergng len a a dvergng len and ray trace a uual.

5 SPH3UW Unt 7.6 Cnvex Lene Page 5 9 The Len Maker Equatn A ueul rmula that requre nly the radu curvature and the cal length and the ndex reractn r the len the len maker equatn n 1 R1 R2 Sgn cnventn r Thn Lene Quantty The Value Ptve When The Value Negatve When Object Lcatn ( ) The Object n rnt the len (th a Real bject) The Object behnd the len (th a Vrtual bject) Image Lcatn ( ) The Image behnd the len (th a Real mage) The Image n rnt the len (th a Vrtual mage) Image heght (h ) The Image n ame rentatn a the bject (uually uprght) The mage n an nverted rentatn a the bject (uually nverted) Radu Curvature R 1 and R 2 The centre curvature n back the len. The centre curvature n rnt the len Fcal Length () We have a Cnvergng Len We have a Dvergng Len The abve chart wll greatly at n the quanttatve calculatn mage lcatn when ray a pang thru lene.

6 SPH3UW Unt 7.6 Cnvex Lene Page 6 9 Example A cnvergng len ha a 20 cm cal length. Determne the mage lcatn and magncatn when the bject : a) 50 cm b) 20 cm c) 15 cm d) -40 cm Slutn: a) 50cm 20cm 33.3cm m 33.3cm 50cm 2 3 b) 200cm 20cm m cm 20cm

7 SPH3UW Unt 7.6 Cnvex Lene Page 7 9 c) 15cm 20cm m 60cm 60.0cm 15cm 4 d) 40cm 20cm 13.3cm m 13.3cm 40cm 1 3 Example A cnvergng gla len (n = 1.50) ha a cal length 30.0 cm n ar. Fnd t cal length when t ubmerged n water, whch ha an ndex reractn 1.33.

8 SPH3UW Unt 7.6 Cnvex Lene Page 8 9 Slutn: Th a jb r the Len Maker equatn. In bth tuatn the len tel de nt change, R 1 and R 2 reman the ame nlen 1 ar R1 R nlen 1 water R1 R2 Each tuatn ha a derent medum r the ray t travel thrugh bere and ater the len, therere we can ue: 1 n len medum nmedum R1 R2 I we dvde thee tw equatn and thu remve the radu curvature term, we btan 1 ngla n ar ar R1 R2 1 ngla water n R R water ar water 1 2 n n n n gla ar gla water 1 1 We nw mply can ubttute knwn value and lve r water water 1 30cm water 30 cm cm The cal length n the water then abut 117 cm. Nte: The cal length any len ncreaed by a actr mmered n a lud, where materal t that the urrundng materal. n n len rat 1 1 when the len n rat the rat the ndex reractn len n the len

9 SPH3UW Unt 7.6 Cnvex Lene Page 9 9 Extra Nte and Cmment