16.226 Useful Information
n n! n! − n
+ =
s s!
R
Gauss’ Formula:
1 1
2 1
+ ! =− =
s s
R
f
"
!
1
1
1
= (n − 1)
−
f
R1 R2
Reflection Formula:
Lens Maker’s Formula:
Ray Transfer Matrices
Refraction at spherical surface: M =
!
"
1L
01
Translation:
M=
Thin lens:
"
1 0
M=
− 1f 1
!
Interference in a thin film:
Two source interference:
!
1
0
n−n" n
n" R n"
"
4π
δ = n f t cos θt + δr
λ0
√
I = I1 + I2 + 2 I1 I2 cos δ
Thin lens:
m=−
ns"
n"s
1 1 1
+ =
s s!
f
1
1
1
L
= + −
f
f1 f2 f1 f2
Telescope, final image at infinity, M = − fo/ fe
!
"
1 0
Reflection at spherical surface: M =
− 1f 1
!
"
AB
f = -1/C
M=
CD
Principal planes (+ to the right): H1 at r = f (1 − D)
H2 at s = f (A − 1)
1
4r2
Fabry-Perot: T =
,F=
(1 − r2 )2
1 + F sin2 (δ/2)
Flat Petzval surface: n1 f1 + n2 f2 = 0
n − nC
Condition for zero chromatic aberration in a 2 lens system: Δ1 f2 + Δ2 f1 = d(Δ1 + Δ2), where Δ = F
nD − 1
!
"2
1.22λ
sin β
πb
Circular aperture: Δθmin =
Single slit diffraction: I(θ) = I0
, β=
sin θ
D
β
λ0
!
"2 !
"2
sin Nα
sin β
πd
Phase velocity, v p = ω/k
Diffraction from N slits: I(θ) = I0
, α=
sin θ
sin α
β
λ0
Group velocity, vg = dω/dk