FORMULAS

Question 1

Lens maker’s formula

Answer 1

F = (n’ - n)
————
r

F: refracting power of surface
n: index of refraction primary medium
n’: index of refraction of secondary medium
r: radius of curvature (in meters)

Question 2

Convert snellen acuity to cycles per degree

Answer 2

600/snellen acuity = cycles per degree

Question 3

Power of mirrors

Answer 3

P = - 2n
———
r

P: power
n: refractive index of surrounding
r: radius of curvature of mirror in meters

** convex mirrors have (+) radius, (-) power

** concave mirrors have (-) radius, (+) power

Question 4

Javal’s rule

Answer 4

Refractive astigmatism = 1.25 x 🔼K

+0.50 for ATR
-0.50 for WTR

Question 5

JND

Answer 5

Snellen denominator
——————————— = x
100

x/2 = (+/- JND)

show patient trial frame

Question 6

Optotype —> find snellen VA

Answer 6

Question 7

Conversion reduced snellen to point notation

Answer 7

Divide denominator by 6

Example: RS 20/30
30/6 = 5 point

Question 8

Formula to determine diopter value of the lens
Example: microscope is 5X, what is the power of the lens in diopters?

Answer 8

M = DLens
————
4

M: magnification
DLens: power of lens in diopters

Example: 5 = F/4
5x4= 20 D

Question 9

Accommodative convergence/ accommodation

Answer 9

AC/A ratio = PD + near (near phoria - far phoria)

PD in cm
Near in meters
EXO (-)
ESO (+)

Question 10

Sheard’s criterion

Answer 10

S = 2/3D - 1/3R

D: phoria
R: compensating fusional vergence

EXO: BO blur
ESO: BI blur

Question 11

Rated magnification/effective magnification

Answer 11

M = d x F

M: magnification
d: object distance (in meters)
F: focal power of the lens

Example:
Holds Homework at 20cm
Uses +16D hand magnifier
What is the magnification of this near optical system?

M = (0.20) x (+16) = 3.2x

*represents change in retinal image size produced by magnifier lens

Question 12

MBS

Answer 12

MBS = ED + TLD + 2 mm

MBS: minimum blank size
ED: effective diameter (given)
TLD: total lens decentration
2mm: allows for possible defects of the edge of the lens that may be present in the lens blank

TLD= |(A+ DBL) - PD|

Question 13

What is the center thickness of RGP with power of +3.50D?

Answer 13

0.27 mm

CT= (0.023 x CL PWR) + 0.19mm
CT: center thickness

0.023 x 3.50 =0.0805
0.0805 + 0.19=0.271 mm

Question 14

What is the minimum center thickness of an RGP?

Answer 14

0.12mm

Question 15

Total transmittance

Answer 15

T = T1 x T2

(Multiply in decimal)

Example:
T1: 80%
T2: 75%

T= 0.80 x 0.75 = 0.6 x100 = 60%

Question 16

Anti-reflective coating

Answer 16

Question 17

Reflectance

Answer 17

Question 18

Galilean telescope

Answer 18

Objective lens positive
Ocular lens negative
Exit pupil inside telescope
FOV is small
Mag up to 4x

Question 19

Keplerian telescope

Answer 19

Objective and ocular lens is positive
Exit pupil outside telescope (lines up with entrance pupil of eye)
FOV is large
Mag is up to 10x

Question 20

A1C conversion to FBS

Answer 20

(A1c x 28.7) -46.8

Example:
A1c = 6.7
FBS = ?

(6.7 x 28.7) - 46.8 =145.49

Question 21

Formula to calculate center thickness of an RGP

Answer 21

CT = (0.023 x CL power) + 0.19mm

Question 22

BC/BCR formula

Answer 22

BC = 337.5/BCR

Question 23

Snell’s law of reflection

Answer 23

n sin() = n’sin()’

Question 24

Power mag (Mp) formula

Answer 24

Mp = 1
———
( 1 - h (FV)

Mp: power mag
h: vertex
FV: back vertex power

Question 25

Shape magnification (Ms) formula

Answer 25

Ms= 1 ——— [(1-F1)(tc/n)] F1: power of front surface tc: center thickness (in meters) n: index of refraction of lens

Question 26

Reading cap formula

Answer 26

Reading cap = 1/ WD WD: working distance in cm

Question 27

Overall power of telescope with reading cap

Answer 27

Overall power = reading cap power x telescope mag Reading cap power = 1/Working distance

Question 28

Mag of telescope

Answer 28

M= overall power/ 4 Or M= - dEntrance pupil ———————- dEXIT pupil **minus sign!!!

Question 29

Formula to calculate diameter of exit pupil (when given telescope marking) Example: what is the diameter of exit pupil for a hand held telescope marked 6x18?

Answer 29

Exit pupil = diameter of objective lens(mm)/ mag Explanation: Mag: 6 Objective lens: 18 Exit pupil = 18mm/6 =3 mm

Question 30

Formula for CCTV equivalent power

Answer 30

D= Mscreen x Dadd D: equivalent power M: mag on screen Dadd: near add power