University Physics Volume 3

# Key Equations

### Key Equations

 Image distance in a plane mirror $do=−dido=−di$ Focal length for a spherical mirror $f=R2f=R2$ Mirror equation $1do+1di=1f1do+1di=1f$ Magnification of a spherical mirror $m=hiho=−didom=hiho=−dido$ Sign convention for mirrors Focal length f $+for concave mirror−for convex mirror+for concave mirror−for convex mirror$ Object distance do $+for real object−for virtual object+for real object−for virtual object$ Image distance di $+for real image−for virtual image+for real image−for virtual image$ Magnification m $+for upright image−for inverted image+for upright image−for inverted image$ Apparent depth equation $hi=(n2n1)hohi=(n2n1)ho$ Spherical interface equation $n1do+n2di=n2−n1Rn1do+n2di=n2−n1R$ The thin-lens equation $1do+1di=1f1do+1di=1f$ The lens maker’s equation $1f=(n2n1−1)(1R1−1R2)1f=(n2n1−1)(1R1−1R2)$ The magnification m of an object $m≡hiho=−didom≡hiho=−dido$ Optical power $P=1fP=1f$ Optical power of thin, closely spaced lenses $Ptotal=Plens1+Plens2+Plens3+⋯Ptotal=Plens1+Plens2+Plens3+⋯$ Angular magnification M of a simple magnifier $M=θimageθobjectM=θimageθobject$ Angular magnification of an object a distanceL from the eye for a convex lens of focal lengthf held a distance ℓ from the eye $M=(25cmL)(1+L−ℓf)M=(25cmL)(1+L−ℓf)$ Range of angular magnification for a givenlens for a person with a near point of 25 cm $25cmf≤M≤1+25cmf25cmf≤M≤1+25cmf$ Net magnification of compound microscope $Mnet=mobjMeye=−diobj(feye+25cm)fobjfeyeMnet=mobjMeye=−diobj(feye+25cm)fobjfeye$