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