Formulas Flashcards
Paraxial Vergence
L’ = L + F
Linear Magnification
h’ = h x m = h x L/L’
Umbra (u + p)
u = h x X / y
Penumbra
p = s (x - y) / y
Prentice’s Rule
P = cF
Snell’s Law
n sin i = n’ sin i’
Critical Angle
Sin ic = 1/n
(given ic) =
n = 1/sin ic
Relative Curvature
RC = nold - 1 / nnew -1
% = (1-RC) x 100
Thin Lens Theory
F = F1 + F2
Velocity/wavelength/frequency
v = f x w
f = v / w
w = v / f
Accurate Sag
s = r - v(r2 - y2)
Approx Sag
s = y2 x F/ 2000 (n - 1)
Power effectivity
F eff = F/ 1 - dF
n’ (given F, r and n)
n’ = F x r +n
Ray Trace Steps (object & image)
f = -n / F
L = n / l
L’ = L + F
l’ = n’ / L’
h’ = h x m = h x L/L’
Lateral Displacement
t x sin (i1 - i1’) / cos i1’
Horizontal Displacement
(tan i1 x t) - (tan i1’ x t)
Real and Apparent Depth
t’/t = n’/n
rearranged:
t1’ = n’ x t1 / n1
Illuminance
E = i/ d2
Illiminance at an angle
E = i / d2 x cos Ø
V d2 + d12
then
d1 / answer = Ø
Centre Thickness
Plus lens:
t = e + s
Minus lens:
e = t + s
Surface Powers
F = n’ - n / r
Transverse Chromatic Aberration
TCA = c F / V
Pinhole Camera
h’/l’ = h/l
rearranged:
h’ = h x l’ / l
