Formulas Flashcards
Paraxial vergence
L’ = L + F
Linear magnification
h’ = h x m or h x L/L’
Umbra (point source)
U = h x (L + L’) / L
Penumbra
P = s x L’ / L
Umbra (extended source)
U = (U + P) - P
Image size (extended source)
h’ = (U+P) + P
Prentices 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 = n old-1 / n new-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
f = -n / F
L = n / l
L’ = L + F
l’ = n’ / L
h’ = h x L/L’
Lateral displacement
t x sin (i1 - i1’) / cos i1’
Horizontal displacement
(tan i x t) - (tan i’ x t)
Lateral deviation
t x sin (i - i’) / cos i’
Apparent depth
BB’ = d x (1 - 1 / n )
Angle of deviation
d = i - i’
Absolute refractive index
3 x 10ms -1 / velocity of light in a medium
Relative refractive index
Velocity of light in medium 1 / velocity of light in medium 2
Height of image
h’ = h x L’/L
Total deviation
D = d1 + d2
d1 = i1 - i1’
d2 = i2’ - i2
Radius (front)
r1 = n’ - 1 / F1
Radius (back)
r2 = 1 - n’ / F2
Edge thickness
e = t + s
Centre thickness
t = e + s
Edge thickness (meniscus)
e = t + s2 - s1
Centre thickness (meniscus)
t = e + s1 - s2
Curved mirrors (step along)
F = r / 2
F = -n / f
L = n / l
L’ = L + F
l’ = -n / L’
h’ = h x L / L’
Minimum Plate Thickness (MPT)
S = t - e
F = 2000 (n - 1) x S / y2
Image size
h’ = h x L / L’
Prentice’s Rule (prismatic effect)
P = cF
The tangent scale
Prism dioptres: x = P x y / 100
Degrees of diopters: x = y x tan 1
Degrees of apical angle: d = (n - 1) a
x = y x tan d
