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Derivelensmaker'sformulafora convexlens. |
Answer» Solution :Lensmaker.sformula LET`r_(1) and r_(2)`be theradiiof curvatureof thethinlens . Let Obe thepointat adistanceu fromthepoleof thefirstcurvedsurfaceof thelens. Realimageis FORMEDAT I.at a distancev.fromthepole`P_(1)`thisimageis formedin thedensermedium. Weknowthat FROMTHE refractionformula , `(n_1)/(-u )+(N_2)/(v)=(n_2-n_1)/(r )i.e.,(n_1)/(-u)+(n_2)/(v.)=(n_2-N_(1))/(r_1)` Where`n_1`is therefractiveindexofrarermediumand ` n_(2)`thatof thedensermedium`(n_(2)gt n_(1))`, FOrthe secondsurface, realimageat I.willserveas - ve. Theobjectspaceis thelensme - diumfor refractivethroughthe secondcurvedsurface. finalimageis formedin AIRAT Iandat adistanceof .v.from ` P_(2)` ` (n_1)/(-u)+(n_2)/(v)=(n_2-n_1)/(r )` ` i.e.,(n_2)/(-v)+(n_1)/(v)=(n_(2)-n_(1))/(-r_2)` Adding (1)and (2)we get ` (n_1)/(-u ) +(n_1)/(v)=(n_2-n_1)((1)/(r_(1))-(1)/(r_(2)))` ` or(1)/(-u )+(1)/(v)=(n_(2)-n_(1))/(n_(1))((1)/(r_(1))-(1)/(r_(2)))` when`u= oo , v= f` when `u=f , v=oo` ` therefore` Thetermon the L.H.Scan bereplacedby ` (1)/(f)`wheref is thefocallengthof lens . `i.e.,(1)/(f)=((n_2-n_1)/(n_1))((1)/(r_1)-(1)/(r_(2)))` Theequation(4)is calledthe lensmaker.sformula Note:(1)usingtheequation(4) ,it canbe shownthat `""_(1) N_(2)= 1-[(r_1r_2)/(f(r_1-r_(2)))]` where ` ""_(1)N_(2)=(n_(2))/(n_(1))` (2)forradiusof curvaturethe letter.R.may beused . |
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