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University Physics Volume 3

# Key Equations

### Key Equations

 Image distance in a plane mirror $do=âˆ’dido=âˆ’di$ Focal length for a spherical mirror $f=R2f=R2$ Mirror equation $1do+1di=1f1do+1di=1f$ Magnification of a spherical mirror $m=hiho=âˆ’didom=hiho=âˆ’dido$ Sign convention for mirrors Focal length f $+for concave mirrorâˆ’for convex mirror+for concave mirrorâˆ’for convex mirror$ Object distance do $+for real objectâˆ’for virtual object+for real objectâˆ’for virtual object$ Image distance di $+for real imageâˆ’for virtual image+for real imageâˆ’for virtual image$ Magnification m $+for upright imageâˆ’for inverted image+for upright imageâˆ’for inverted image$ Apparent depth equation $hi=(n2n1)hohi=(n2n1)ho$ Spherical interface equation $n1do+n2di=n2âˆ’n1Rn1do+n2di=n2âˆ’n1R$ The thin-lens equation $1do+1di=1f1do+1di=1f$ The lens makerâ€™s equation $1f=(n2n1âˆ’1)(1R1âˆ’1R2)1f=(n2n1âˆ’1)(1R1âˆ’1R2)$ The magnification m of an object $mâ‰¡hiho=âˆ’didomâ‰¡hiho=âˆ’dido$ Optical power $P=1fP=1f$ Optical power of thin, closely spaced lenses $Ptotal=Plens1+Plens2+Plens3+â‹¯Ptotal=Plens1+Plens2+Plens3+â‹¯$ Angular magnification M of a simple magnifier $M=Î¸imageÎ¸objectM=Î¸imageÎ¸object$ Angular magnification of an object a distanceL from the eye for a convex lens of focal lengthf held a distance â„“ from the eye $M=(25cmL)(1+Lâˆ’â„“f)M=(25cmL)(1+Lâˆ’â„“f)$ Range of angular magnification for a givenlens for a person with a near point of 25 cm $25cmfâ‰¤Mâ‰¤1+25cmf25cmfâ‰¤Mâ‰¤1+25cmf$ Net magnification of compound microscope $Mnet=mobjMeye=âˆ’diobj(feye+25cm)fobjfeyeMnet=mobjMeye=âˆ’diobj(feye+25cm)fobjfeye$
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