Formulae

Question 1

How to calculate relative curvature of a lens

Answer 1

RC= n_old-1 / n_new-1

Question 2

Calculate the percentage of thickness reduction of a lens when comparing refractive indicies

Answer 2

(1-RC) x 100

Question 3

Vergences
l₁ = infinity
l₁ = 1/L₁

Answer 3

l₁’ = 1/L₁’
L₁’ = L₁+F₁
l₂ = l₁‘-t/n
L₂ = 1/l₂
F₂ = L₂‘-L₂
L₂’ = L₂+F₂

Question 4

Calculate resultant prism

Answer 4

PR = √ v²+h²

Question 5

Calculate the refractive index of a lens

Answer 5

n= n/n’

Question 6

Calculate the surface power of a lens

Answer 6

F= n’-n / r

Question 7

Calculate wavelength

Answer 7

v= fλ
where:
v=velocity
f=frequency
λ=wavelength

Question 8

Calculate critical angle

Answer 8

sin i_c = 1/n

Question 9

Snell’s law

Answer 9

n sin i = n’ sin i’
OR
Sini’ = n/n’ x Sini

Question 10

Formula regarding thin lens theory, where:
F₁=Front surface power
F₂=Back surface power
F=Total surface power

Answer 10

F= F₁+F₂

Therefore:
F₂= F-F₁

Question 11

Deviation of a prism
where:
p=prism power measured in dioptres

Answer 11

p=displacement(cm) / distance(m)

Question 12

Calculate deviation with a given apical angle
where:
n=index of a prism
a=apical angle in degrees
d=deviation produced in degrees

Answer 12

d= (n-1)a

Question 13

Calculation for finding prismatic power

Answer 13

P= 100 tan d

Question 14

Prentice’s rule

Answer 14

P=cF

Question 15

Accurate Sag Formula
where:
s= sag (mm)
r= radius of curvature (mm)
y= half chord length (mm)

Answer 15

s= r - √(r²-y²

Question 16

Calculate radius of curvature

Answer 16

r = (n’ - n)/F

Question 17

Calculate centre thickness of a plus lens
where:
t=centre thickness
s=sag of the front surface
e=edge thickness

Answer 17

t= e+s

Question 18

Calculate centre thickness of a minus lens
where:
t=centre thickness
s=sag of the front surface
e=edge thickness

Answer 18

t=e-s

Question 19

Calculation for spectacle magnification

Answer 19

K=1/k (k must be in meters)
SM=K/F

Question 20

Calculation to find the amount of Transverse Chromatic Aberration on a lens
Where:
c= distance from the optical centre of the lens (cm)
F= lens power
V= V-value of the lens

Answer 20

TCA= cF / v

Question 21

Calculate angle of deviation

Answer 21

d= i - i’

Question 22

Horizontal displacement

Answer 22

(tan i x t) – (tan i’ x t)

Question 23

Vertical displacement

Answer 23

t x Sin (i - i’) / Cos i’

Question 24

Find the height of an image

Answer 24

h’ = (L/L’) x h

Question 25

Find magnification of an image

Answer 25

m = L/L' = h’/h

Question 26

Thin lens theory

Answer 26

F = F1 + F2 therefore F2 = F - F1

Question 27

Prism with apical angle over 10 degrees

Answer 27

Sin i1’ = n / n’ x Sin i1 i2 = a – i1’ Sin i2’ = n / n’ x Sin i2 d = (i1 + i2’) – a

Question 28

Minimum deviation

Answer 28

i₁ = i₂'

Question 29

Formula for calculating illuminance

Answer 29

E (Illuminance) = Ø (Luminous Flux) / A (size of area on surface covered)

Question 30

Formula for calculating luminous intensity

Answer 30

i (Luminous Intensity) = Ø (Luminous Flux) / w (Solid Angle)

Question 31

Formula for calculating luminous intensity with a given direction

Answer 31

i =dØ / dw

Question 32

Inverse square law of illuminance formula

Answer 32

E = i / d²

Question 33

Cosine law of illuminance formula

Answer 33

E = (I / d²) cosA

Question 34

What is the focal length of a mirror?

Answer 34

Half of its radius f=r/2

Question 35

To transpose from crossed cyl form to sphere cyl form: +4.00DC x 180/ +6.00DC x 90

Answer 35

i. Write the first cylinder as the sphere i.e. +4.00DS ii. Subtract the 1st cylinder from the 2nd cylinder to give the cylinder power i.e. +2.00DC iii. The axis is that of the 2nd cylinder i.e. 90 +4.00DS / +2.00DC x 90

Question 36

To transpose from one sphere/cyl form to its alternate sphere cyl form: +4.00DS / +2.00DC x 90

Answer 36

i) Add sphere and cyl together to give new sphere power i.e. +6.00DS ii) Change the sign of the cyl i.e. –2.00DC iii) Rotate the axis through 90 i.e. 180 +6.00DS / -2.00DC x 180

Question 37

To transpose from sphere/cyl form to crossed cyl form: +6.00DS / +2.00DC x 180

Answer 37

i) Write the sphere as the first cylinder with its axis perpendicular to the axis in the given Rx i.e. +6.00DC x 90 ii) To find the second cylinder, add together the sphere and cylinder in the given Rx i.e +8.00DC iii) The axis of the second cylinder is the axis in the given Rx i.e. 180 +6.00DC x 90 / +8.00DC x 180

Question 38

To transpose onto a given base curve +1.00DS / -3.00DC x 90 onto a +6.00D base curve

Answer 38

i. Ensure the base curve and the cylinder in the Rx have the same sign. If not transpose to its alternate sph/cyl form: +1.00DS / -3.00DC x 90 transposed is -2.00DS / +3.00DC x 180. Now use the transposed Rx. ii. Write the base curve with its axis perpendicular to that in the Rx: +6.00DC x 90 as the base curve is positive, it is written above the line. iii. To find the cross curve, add the cylinder in the Rx to the base curve keeping the axis as in the prescription +6.00 + 3.00 = +9.00DC x 180. The cross curve is always written on the same line as the base curve. iv. To find the sphere curve, subtract the base curve from the sphere in the Rx: -2.00 – 6.00 = -8.00DS. The sphere curve is minus so is written below the line.

Question 39

To transpose onto a given sphere curve rules -1.50 / -2.00 x 60 onto a -8.00D sphere curve

Answer 39

i) Transpose the given sph cyl rx to the same sign as the base curve, so if the sphere curve is minus the base curve must be a plus value So, we have -3.50 / +2.00 x 150, we call this the prescription used. ii) Subtract the given sphere curve from the sphere of the prescription used to get the base curve, so -3.50 - -8.00 = +4.50 write this as a cylinder (DC) with its axis at 90 degrees to that of the prescription used. iii) Add the cylinder of the prescription used to the base curve to give us the cross curve, use the axis from the prescription used

Question 40

Approximate Sag formula:

Answer 40

yF / 2000 (n-1)