2. Spherical Lenses Flashcards
a = sin(a) is known as? When is it used?
First order theorem. Used with paraxial rays.
What do the following letters represent?
i(‘), u(‘), O(‘), y, g, l(‘), n(‘), r. What needs to be taken into account in calculations?
(paraxial)
i = normal to ray
u = ray to axis
O = object/(image)
y = height
g = normal to axis
l = focal length
n = refractive index
r = radius
**beware of signs of angles and length directions.
c(curvature) = ?
1/r
r = radius
In paraxial refraction formula, ni = ?
n’i’
In diagram, triangle OPC, i = ? (paraxial)
g - u
(normal to axis) - (ray to axis)
-u due to angle direction.
In diagram, triangle PCO’, g = ? (paraxial)
u’ + i’
(ray to axis) + (normal to ray)
n’u’ - nu =? (paraxial)
yc(n’-n)
Surface power F = c…?
c(n’-n)
In paraxial calculations, y/l(‘) is approx. equal to?
sin(u(‘))
(should technically be tan)
F = ? (second form of paraxial formula)
n’/l’ – n/l
F = ? (third form paraxial formula)
L’ – L
(n/l, n’/l’ called reduced vergences L, L’)
L, L’ also expressed as? (paraxial)
n/l, n’/l’ called reduced vergences L, L’
F is measured in?
F in dioptres (m-1)
Symbol for dioptres is D.
r = ? (sag of a surface)
(y^2 + s^2)/(2s)
s = ? (sag of a surface)
s = r ± √(r2 – y2)
From eq. (2.2), taking s^2 as being small
s ~ y^2/(2r) ~ ? (sag of a surface)
y^2c/2
In sag of surface, s represents?
Surface of lens to point where y intersects with principle axis.
If nI = 1.53, FI = +10.00 D, n = 1.70, what is F?
Lens measure
Answer: Using F = (n – 1)F(instrument)/(nI – 1) (eq. 2.5)
F = 0.70 x 10.00/0.53 = +13.2D
Lens effectivity is?
The change in vergence of light that occurs at different points along its path. This is related to vertex distance.
Can usually assume thin lens when…
Lens is concave thus thin in centre. Therefore reasonable to add surface power for power F.
