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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 mirrorfor convex mirror+for concave mirrorfor convex mirror
Object distance do +for real objectfor virtual object+for real objectfor virtual object
Image distance di +for real imagefor virtual image+for real imagefor virtual image
Magnification m +for upright imagefor inverted image+for upright imagefor inverted image
Apparent depth equation hi=(n2n1)hohi=(n2n1)ho
Spherical interface equation n1do+n2di=n2n1Rn1do+n2di=n2n1R
The thin-lens equation 1do+1di=1f1do+1di=1f
The lens maker’s equation 1f=(n2n11)(1R11R2)1f=(n2n11)(1R11R2)
The magnification m of an object mhiho=didomhiho=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 distance
L from the eye for a convex lens of focal length
f held a distance from the eye
M=(25cmL)(1+Lf)M=(25cmL)(1+Lf)
Range of angular magnification for a given
lens for a person with a near point of 25 cm
25cmfM1+25cmf25cmfM1+25cmf
Net magnification of compound microscope Mnet=mobjMeye=diobj(feye+25cm)fobjfeyeMnet=mobjMeye=diobj(feye+25cm)fobjfeye
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