formulas optics

Vergence

L = n / l

Distance from vergence

l = 1 / L

Parallel rays

L = 0

Refraction Snell’s Law

n1 * sin(theta1) = n2 * sin(theta2)

Critical angle

theta_c = arcsin(n2 / n1)

Vergence relationship

L' = L + F

Power-focal length relationship

F = 1 / f'

Thin lens equation

(1 / l') - (1 / l) = (1 / f')

Magnification

M = l' / l

Image height

h' = M * h

Surface power

F = (n' - n) / r

Surface vergence equation

L' = L + F

Surface focal length

f' = n' / F

Thin prism deviation

d = (n - 1) * A

Thick prism deviation

d = i1 + i2 - A

Prism diopters

P = 100 * tan(d)

Linear prism formula

P = 100 * (x / y)

Prentice’s Rule

P = c * F

Mirror power

F = -2 / r

Mirror vergence

L' = L + F

Mirror image distance

l' = 1 / L'

Mirror magnification

M = l' / l

Mirror focal length

f = r / 2

Plane mirror vergence

L' = -L

Plane mirror image distance

l' = -l

Thick lens equivalent power

Fe = F1 + F2 - (t/n) * F1 * F2

Front surface power

F1 = (n - 1) / r1

Back surface power

F2 = (1 - n) / r2

Thick lens step 1

L1 = 1 / l

Thick lens step 2

L1' = L1 + F1

Thick lens step 3

l2 = l1' - t

Thick lens step 4

L2 = n / l2

Thick lens step 5

L2' = L2 + F2

Thick lens step 6

l' = 1 / L2'

Thick lens magnification

M = l' / l