Formulae and defintions Flashcards
How to calculate relative curvature of a lens
RC= nold-1 / nnew-1
Calculate the percentage of thickness reduction of a lens when comparing refractive indicies
(1-RC) x 100
Vergences
l1 = infinity
l1 = 1/L1
l1’ = 1/L1’
L1’ = L1+F1
l2 = l1‘-t/n
L2 = 1/l2
F2 = L2‘-L2
L2’ = L2+F2
Calculate resultant prism
PR = √ v²+h²
Calculate the refractive index of a lens
n= n/n’
Calculate the surface power of a lens
F= n’-n / r
Calculate wavelength
v= fλ
where:
v=velocity
f=frequency
λ=wavelength
Calculate critical angle
sin ic = 1/n
Snell’s law
n sin i = n’ sin i’
OR
Sini’ = n/n’ x Sini
Formula regarding thin lens theory, where:
F1=Front surface power
F2=Back surface power
F=Total surface power
F= F1+F2
Therefore:
F2= F-F1
Deviation of a prism
where:
p=prism power measured in dioptres
p=displacement(cm) / distance(m)
Calculate deviation with a given apical angle
where:
n=index of a prism
a=apical angle in degrees
d=deviation produced in degrees
d= (n-1)a
Calculation for finding prismatic power
P= 100 tan d
Prentice’s rule
P=cF
Accurate Sag Formula
where:
s= sag (mm)
r= radius of curvature (mm)
y= half chord length (mm)
s= r - √(r2-y2
Calculate radius of curvature
r = (n’ - n)/F
Calculate centre thickness of a plus lens
where:
t=centre thickness
s=sag of the front surface
e=edge thickness
t= e+s
Calculate centre thickness of a minus lens
where:
t=centre thickness
s=sag of the front surface
e=edge thickness
t=e-s
Calculation for spectacle magnification
K=1/k (k must be in meters)
SM=K/F
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
TCA= cF / v
Calculate angle of deviation
d= i - i’
Horizontal displacement
(tan i x t) – (tan i’ x t)
Vertical displacement
t x Sin (i - i’) / Cos i’
Find the height of an image
h’ = (L/L’) x h
Find magnification of an image
m = L/L’ = h’/h
Thin lens theory
F = F1 + F2 therefore F2 = F - F1
Prism with apical angle over 10 degrees
Sin i1’ = n / n’ x Sin i1
i2 = a – i1’
Sin i2’ = n / n’ x Sin i2
d = (i1 + i2’) – a
Minimum deviation
i1 = i2’
What is luminous flux?
This is the quantity of light energy coming from a source that is capable of producing a
visual sensation. Luminous flux is measured in lumens (lm).
Define illuminance
When light flows from a source and reaches a surface, the surface is said to be illuminated.
The amount of illumination will depend on the strength of the source (luminous flux) and the distance of the source to the surface and the area covered. Illuminance is measured in lumens per square metre, also called lux
Formula for calculating illuminance
E (Illuminance) = Ø (Luminous Flux) / A (size of area on surface covered)
What is luminous intensity?
This measures the ability of a source to produce light in a given direction. It is the luminous flux emitted in a narrow cone containing the direction divided by the solid angle of the cone
Formula for calculating luminous intensity
i (Luminous Intensity) = Ø (Luminous Flux) / w (Solid Angle)
Formula for calculating luminous intensity with a given direction
i =dØ / dw
Define Luminance
Also known as brightness, this is the intensity of light emitted in a given direction for a certain area. This is expressed as candelas per square metre.
define luminance efficacy
This is the amount of light produced by a source for each watt of power consumed. It is used
to compare the efficiency of one lamp to another and is measured in lumens per watt
What is the Inverse Square Law of Illuminance
The illuminance at a point on a surface is
inversely proportional to the square of the distance between the point and the source.
What is the Cosine law of illuminance
If the normal to an illuminated surface is at an angle to the direction
of the incident light, the illuminance is proportional to the cosine of the angle
Inverse square law of illuminance formula
E = i / d2
Cosine law of illuminance formula
E = (I / d2) cosA
What is the First Law of Refraction?
The incident ray and the refracted ray lie in the same plane which is normal to the refracting surface at the point of refraction
What is the Second Law of Refraction?
The ratio of the sine of the incident angle is constant for any two media and for monochromic lens only
What is the focal length of a mirror?
Half of its radius
f=r/2
To transpose from crossed cyl form to sphere cyl form:
+4.00DC x 180/ +6.00DC x 90
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
To transpose from one sphere/cyl form to its alternate sphere cyl form:
+4.00DS / +2.00DC x 90
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
To transpose from sphere/cyl form to crossed cyl form:
+6.00DS / +2.00DC x 180
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
To transpose onto a given base curve
+1.00DS / -3.00DC x 90 onto a +6.00D base curve
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.
To transpose onto a given sphere curve rules
-1.50 / -2.00 x 60 onto a -8.00D sphere curve
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
Approximate Sag formula:
y<sup2</sup>F / 2000 (n-1)
