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’
sin i’ = n / n’ x sin i
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

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

e=t+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’