Phys223
Equations for Chapters 23 and 24
Reflection: i  r
Mirror/Thin Lens Equation
1
1
1


f
do di
Refraction: n1 sin 1  n2 sin 2
n
c
v
Glasses: Lens power P 
Lens Maker’s Equation
1
diopters
f
1 1 
1
  n  1   
f
 R1 R2 
Sign Conventions
The mirror equation and the thin lens equation work for both convex and concave mirrors and lenses if
you use the correct sign conventions.
Mirrors
Quantity
Object location do
Image location di
Image height hi
Focal length f and radius R
Magnification M
Positive when
Negative when
object is in front of mirror object is in back of mirror
(real object)
(virtual object)
image is in front of mirror image is in back of mirror
(real image)
(virtual image)
image is upright
image is inverted
mirror is concave
mirror is convex
image is upright
image is inverted
Thin Lenses
Quantity
Object location do
Image location di
Image height hi
R1 and R2
Focal length f
Magnification
Positive when
Negative when
object is in front of lens (real object is in back of lens
object)
(virtual object)
image is in back of lens (real image is in front of lens
image)
(virtual image)
image is upright
image is inverted
center of curvature is in back center of curvature is in front
of lens
of lens
converging lens
diverging lens
image is upright
image is inverted
Phys223
Equations for Chapters 23 and 24