Formulae

Question 1

Reflectance percentage for both sides of a lens

Answer 1

R=(n-1)² / (n+1)² x100

Question 2

How to calculate relative curvature of a lens

Answer 2

RC= n_old-1 / n_new-1

Question 3

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

Answer 3

(1-RC) x 100

Question 4

Vergences
l₁ = infinity
l₁ = 1/L₁

Answer 4

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

Question 5

Calculate resultant prism

Answer 5

PR = √ v²+h²

Question 6

Calculate the refractive index of a lens

Answer 6

n= n/n’

Question 7

Calculate the surface power of a lens

Answer 7

F= n’-n / r

Question 8

Calculate wavelength

Answer 8

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

Question 9

Calculate critical angle

Answer 9

sin i_c = 1/n

Question 10

Formula to find refractive index using the critical angle

Answer 10

n= 1/sin i_c

Question 11

Snell’s law

Answer 11

n sin i = n’ sin i’
sin i’ = n / n’ x sin i

Question 12

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

Answer 12

F= F₁+F₂

Therefore:
F₂= F-F₁

Question 13

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

Answer 13

p=displacement(cm) / distance(m)

Question 14

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

Answer 14

d= (n-1)a

Question 15

Calculation for finding prismatic power

Answer 15

P= 100 tan d

Question 16

Prentice’s rule

Answer 16

P=cF

Question 17

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

Answer 17

s= r - √(r²-y²

Question 18

Calculate radius of curvature

Answer 18

r = (n’ - n)/F

Question 19

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

Answer 19

t= e+s

Question 20

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

Answer 20

e=t+s

Question 21

Calculation for spectacle magnification

Answer 21

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

Question 22

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 22

TCA= cF / v