Mirrors and Lenses Summary Page

Law of reflection:

The angle of incidence is equal to the angle of reflection: $\theta$i = $\theta$r

Index of refraction

n = c / v = (speed of light in vacuum) / (speed of light in medium)

Snell's Law

n1 sin $\theta$1 = n2 sin $\theta$2

Critical angle for total internal refelction

$\theta$crit = sin-1(n1/n2) light going from material 2 to material 1

Focal length of a concave mirror

f =R/2

Focal length of a convex mirror

f= -R/2

Mirror or lens equation

1/p + 1/q = 1/f

Magnification of a morror or lens

m = -q/p

Lens maker equation

1/f = (nL-nM)·[1/R1 + 1/R2]

Power of a lens in diopters

D = 1/f; f must be in meters

Table of the four possible cases for mirrors and lenses

p
q
f
M

p>2f

f<q<2f

real

f>0; concave mirror or converging lens

-1<M<0, inverted

reduced

f<p<2f

q>2f

real

f>0; concave mirror or converging lens

M<-1, inverted

enlarged

p<f

q<0

virtual

f>0; concave mirror or converging lens

M>1, upright

enlarged

p>0

q<0

virtual

f<0; convex mirror or diverging lens

M<l, upright

reduced