optics cheat sheet pt 2

Vergence formula

L = n / l

Distance from vergence

l = 1 / L

Parallel rays vergence

L = 0

Sign convention

Left of surface = negative, Right = positive

Snell’s Law

n1·sinθ1 = n2·sinθ2

Critical angle formula

θc = arcsin(n2 / n1)

Lens vergence relationship

L' = L + F

Lens power/focal length relation

F = 1 / f'

Thin lens equation

(1/l') – (1/l) = 1/f'

Magnification formula

M = l'/l

Image height

h' = M·h

Real image condition

L' > 0

Virtual image condition

L' < 0

Surface power formula

F = (n' – n) / r

Vergence across a refracting surface

L' = L + F

Focal length of a refracting surface

f' = n'/F

Thin prism deviation

d = (n – 1)A

Thick prism deviation

d = i1 + i2 – A

Prism diopters formula

P = 100·tan(d)

Linear prism formula

P = 100·(x / y)

Prentice’s Rule

P = c·F

Mirror power formula

F = –2 / r

Mirror vergence equation

L' = L + F

Mirror image distance

l' = 1 / L'

Mirror magnification

M = l'/l

Mirror focal length

f = r / 2

Plane mirror image distance

l' = –l

Plane mirror vergence

L' = –L

Front surface power

F1 = (n – 1) / r1

Back surface power

F2 = (1 – n) / r2

Equivalent thick lens power

Fe = F1 + F2 – (t/n)·F1·F2

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

Principal meridians definition

Two meridians 90° apart with max and min power

Cylinder power

Difference between principal meridians

Power cross purpose

Shows power in each meridian for spherocyl lenses

Transposition step 1

New sphere = S + C

Transposition step 2

Change cylinder sign

Transposition step 3

Rotate axis by 90°

Oblique meridian power formula

F_oblique = S + C·sin²(θ)

Angle for oblique meridian power

θ = |axis – desired meridian|

Sin² 30° value

0.25

Sin² 45° value

0.50

Sin² 60° value

0.75

Spherical equivalent (SE)

SE = S + C/2

Sturm’s conoid vertical line focus

From vertical meridian’s power (L' = L + FV)

Sturm’s conoid horizontal line focus

From horizontal meridian’s power (L' = L + FH)

Distance from vergence of line foci

l = 1 / L'

Circle of least confusion (CLC) vergence

L_CLC' = (LV' + LH') / 2

Hand neutralization: with-motion

Lens is minus

Hand neutralization: against-motion

Lens is plus

Neutralizing spherocylinder rule

Neutralize each meridian separately

Broken line in hand neutralization

Not principal meridian

Intact line in hand neutralization

Principal meridian

Principal meridian orientation

Cylinder axis is the meridian with no cylinder power