Yay for physics exams!

[Shadow]

Yay for over 15 pages of physicsy goodness. Check out my 3/5 complete physics formula sheet:

EDIT: hey cool, some of the symbols actually show up

EDIT EDIT: physics formulas are possibly making me crazy

Fluids
ρ=m/V
p_2=p_top+ρgh
Hydraulic press:
F_2=A_2/A_1  F_1
Buoyancy
Force exerted by pressure difference:
F=(p_a-p_i )A
F_buoy=ρ_fluid gV
F_net=F_g (1-ρ_f/ρ_o )
Submerged object:
F_net=(ρ_f-ρ_o ) V_o g
Floating object:
V = volume of object underwater, buoyant force balances weight exactly
V/V_o =ρ_o/ρ_f →the fraction of the object below the surface
Surface tension (F-36)
γ=F/d
p=p_a+4γ/R

Capillary:
h=2γcosθ/ρgr
Fluid flow:
A_1 v_1=A_2 v_2→volume flow rate
A_1 v_1 ρ_1=A_2 v_2 ρ_2→mass flow rate
p_1+ρgh_1+1/2 ρv_1^2=constant

Venturi meter (F44')
v=√(2gh(ρ_fluid-ρ_liquid )/([(A/a)^2-1] ρ_liquid ))→fluid refers to the measuring device,liquid to the moving liquid
Toricelli
v_b=√2gh
Viscosity
η= FL/Av
R_e=ρvd/η→if≥2000,turbulent.If≤2000,laminar.If 2000≤R_e≤3000,unstable.
Thermodynamics
Zeroth Law:
Two bodies in thermal equilibrium with a third are also in equilibrium with each other.
First Law:
Energy is conserved
Second Law:
Entropy always increases or stays the same in spontaneous processes
Third Law:
T_f=9/5 T_c+32→ΔT_f=9/5 ΔT_c
T_c=5/9 (T_f-32)→ΔT_c=5/9 ΔT_f
Thermal expansion:
ΔL=αL_0 ΔT→L=L_0 (1+αΔT)
α=(ΔL/L_0 )/ΔT
β=3α


Calorimetry and heat transfer:
Q=mcΔT
Q=mL_f
H=kA((T_2-T_1)/L)→k=thermal conductivity constant,A=cross-sectional area,L=length of transfer
R=L/k→H=A(T_2-T_1 )/R→R^' s in⁡〖series are summed〗
Interface transfers:
T=(〖(k〗_1 L_2 T_1+k_2 L_1 T_2))/(k_1 L_2+k_2 L_1 )=(R_2 T_1+R_1 T_2)/(R_1+R_2 )
H=A(T_2-T_1 )/(L_2/k_2 +L_1/k_1 )
Radiation:
P=σAeT^4→σ=5.6696*〖10〗^(-8),A=surface area,0≤e≤1,T(K)
P_net=σAe(T^4-T_0^4 )
Gas transformations:
pV=NkT→N=nN_A,k=R/N_A
C_P-C_V=R→C_V=3/2 R for monatomic,5/2 R for diatomic
γ=C_P/C_V =1.40 for diatomic,1.67 for monatomic
ΔU=nC_V ΔT

Adiabatic:
ΔU=-W,Q=0,W=(P_1 V_1-P_2 V_2)/(γ-1)
pV^γ=constant
TV^(γ-1)=constant
Free expansion:
ΔU=0,Q=0,W=0
Isovolumetric:
ΔU=Q=nC_V ΔT ,Q=3/2 nRΔT=nC_V nΔT ,W=0
Isobaric:
ΔU= nC_P ΔT-p(V_f-V_i),Q= nC_p ΔT,W=p(V_f-V_i)
Isothermal:
ΔU=0,Q=W,W=nRTln(V_f/V_i )
Microscopic Interpretations of pressure:
p=(2/3)(N/V)(1/2 mv^2 )
T=(2/3k)(1/2 mv^2 )
K_kinetic=1/2 kT per degree of freedom
E=f/2 nRT=f/2 NkT=N(1/2 mv^2 )→f=degree of freedom,3 for mono,5 for dia.
v_rms=√(3RT/M)  M=molar mass,carefulof units
v_avg=√(8RT/πM)→average speed,used in all above equations
v_p=√(2RT/M)→most probable speed
f=√2 πd^2 v_avg (N/V)→frequncy of collisions
λ=1/(√2 πd^2 (N/V) )→average free path
N/V=P/kT=(PN_A)/RT
s_avg=1/(N/V)^((1/3) ) →average separation between molecules
Avogadro's equation can be found on Q-57a
Heat engines
Cyclic process means Q=W
Q=W=Q_h-Q_c
e=W/Q_h =1-Q_c/Q_h →heat engine
K_r=Q_c/W=Q_c/(Q_h-Q_c )→refrigerator
Carnot cycle:
Q_c/Q_h =T_c/T_h
K_C=T_c/(T_h-T_c )
e_c=1-T_c/T_h
Otto cycle:
e_o=1-(V_2/V_1 )^(γ-1)=1-T_A/T_B =1-T_D/T_C
Heat pump:
K_HP=Q_H/W=Q_h/(Q_h-Q_c )<T_h/(T_h-T_c )
Entropy:
S=∫_i^f▒dQ/T  (see page Q92+)
dQ=nC_V dT+nRTdV/V
dQ=mcdT→ΔS=mcln(T_F/T_i )
Free expansion:
ΔS=nRTln(V_F/V_i )
W_unavailable=T_c ΔS_universe
ΔS=kNln(V_f/V_i )
W=V_i/V_m →V_m=volume of a molecule
S=klnW where W=W_f/W_i
Electricity:
e=1.60219*〖10〗^(-19)C
mass of e=9.1*〖10〗^(-21)
k=8.9875*〖10〗^9
ϵ_0=8.8542*〖10〗^(-12)
Electric field lines start on positive charges and end on negative ones.
F=(kq_1 q_2)/r^2
E=kq/r^2
Dipoles:
p=2aq      where 2a is the distance separating charges and p points from-to+
τ=p x E=pEsinθ
W=pE(-cosθ+cos⁡〖θ_0 〗)
U=-p x E
Motion in an electric field:
y=eE/(2mv_0^2 ) x^2
Flux:
ϕ=∮▒〖E*dA〗
ϕ_c=q/ϵ_0    set this equal to surface integral to solve for E
Pages E36 + p772 for many examples.
Dipoles:
p=qd and point in direction from negative to positive charge
τ=pEsinϕ=qdEsinϕ=p x E
U(ϕ)= -p*E= -pEcosϕ
W=pEcosϕ_2-pEcosϕ_1
Electric potential:
F=(kq_1 q_2)/r^2
U=(kq_1 q_2)/r
U=k∑_(i<j)^n▒(q_i q_j)/r_ij
ΔU=〖-q〗_0 ∫_i^f▒〖E*ds〗
ΔV=-∫_i^f▒〖E*ds〗 
V=kq/r   for point charge
V=k∑_i▒q_i/r_i =k∫▒dq/r
Capacitance
C=Q/V_ab
Capacitance depends on geometry, proportional to area and inversely proportional to the distance between the plates.
C=(ϵ_0 A)/d  for parallel plate capacitor
In series, the magnitude of the charges is the same on each capacitor:
1/C_eq = ∑_(i=1)^n▒1/C_i
V_eq= ∑_(i=1)^n▒V_i
In parallel, the voltage difference is the same across each capacitor:
C_eq=∑_(i=1)^n▒C_i
Q_eq=∑_(i=1)^n▒Q_i
Potential energy in a capacitor:
U=Q^2/2C=1/2 CV^2=1/2 QV


Energy density in vacuum:
u=1/2 ϵ_0 E^2
Dielectrics:
K=C/C_0
V=V_0/K
E=E_0/K
σ_i=σ(1-1/K)   indiuced surface charge density
ϵ=Kϵ_0   is the permittivity
u=1/2 ϵE^2  and more on page 830
∮▒〖KE*dA=Q_enc/ϵ_0 〗
Work is the area under the Q-V curve. pE79'
Current and Resistance:
I=n|q| v_d A    where n is the particle density m^(-3)
J=n|q| v_d  is the current density   J=I/A
n=ρ(kq/m^3 )/M(kg/mole) *N_A
ρ=E/J    definition of resistivity
ρ(T)= ρ_0 (1+α(T-T_0 ) )
Page 852 for alpha values.
R=ρL/A
V=IR
R(T)= R_0 (1+α(T-T_0 ) )     ΔR=R_0 αΔT

EMF: ϵ=voltage of EMF source
ϵ=V_ab=IR   in ideal EMF sources
V_ab=ϵ-Ir      for sources with internal resistance
V_ab=IR
I=ϵ/(R+r)       R+r=total circuit resistance
P=V_ab I=I^2 R=(V_ab^2)/R    power input to a resistor
P=ϵI-I^2 r    power output of  source
Iϵ=I^2 R+I^2 r
P=ϵI+I^2 R   power input to a source
Metallic conductivity:
v_av=v_d= aτ=qτE/m    where m is mass and τ is the average time between collisions
J=(nq^2 τE)/m=σE
ρ=m/(nq^2 τ)  for resistivity,and conductivity is the reciprocal
In series:
R_eq= ∑_(i=1)^n▒R_i
I=I_1=I_2...=I_n
V_eq= ∑_(i=1)^n▒V_i

In parallel:
1/R_eq = ∑_(i=1)^n▒1/R_i
V=V_1=V_2=V_n
I_eq= ∑_(i=1)^n▒I_i

[Ashyra Nightwing]

:O

Last time I did Physics (GCSEs) I got an A, but I still don't know how...

[The Lady Shael]

Get it away! Take it away! Out!


ahhhhhhh

[bjornredtail]

I don't have the right character set... Or the board isn't set up right.. or.. Meh.

That's a lot of very different stuff... everything from F=MA to fluids and magnetism.

* bjornredtail for a moment wishes he was 'real' engineer

[Shadow]

That's the microsoft word equation editor.

I haven't even started on the sections on light yet.

My physics exam is open book, I can even brig my laptop if I want. Not that it will help me, he likes to ask really tricky qualitative questions.

[windhound]

Laptops?  To a test?!  Are they mad, or just real trusting?
Sharing answers over IM FTW!

I always hate open book exams.  It gives the teachers an excuse to make the tests as hard as they can

And lol, are you a fake engineer Nev?
I'm Electrical and I have an impulse to get a flamethrower and kill it with fire

[Shadow]

I think they draw the line at active internet connections, so no IM, sadly.

[Shadow]

Today' additions, about 3/4 done now.

Light:
c=2.9979*〖10〗^8  m/s
n=c/v
θ_i=θ_r  for plane mirrors
n_1 sinθ_1=n_2 sinθ_2
λ=λ_0/n
sinθ_crit=n_b/n_a   for n_b>n_a  and n_b  the index of the resultant medium
Polarization:
I=I_0/2  for unpolarized light becoming polarized
I=I_0  cos^2⁡θ for polarised light passing through an analyzer
tanθ_p=n_b/n_a    reflected light is completely polarized perpendicular to the plane of incidence
For θ_p the reflected and refracted beams are perpendicular and the refracted beam is partially polarized parallel to the plane of incidence.
I_blue/I_red ≈ 9.4   
I ~ 1/λ^4   light is most strongly polarized if it is seen perpendicular to it path of travel
Geometric optics:
Sign conventions:
s>0 if object is on incoming light side.
s^' is positive if it is on the opposite side as s
C>0 if C is on the outgoing light side of the surface (positive for concave, negative for convex, see pg 1611)
m=y^'/y=-s^'/s  if m<0,image in inverted

Spherical reflective surfaces:
any ray passing through C is reflected back on itself
any ray passsing through f is reflected parallel and any parallel ray is reflected through f
any ray to the vertex reflects symmetrically around optic axis
1/s+1/s^' =2/R=1/f
Refraction at spherical interface:
n_a/s+n_b/s^' =(n_b-n_a)/R
m=y^'/y=-(n_a s^')/(n_b s)
for convex refracting surface,R>0 since it is on the same side as outoign rays,see 1171.
Thin lenses:
1/s+1/s^' =1/f
m=-s^'/s
See 1176 for various names of lens combinations
1/f=(n-1)(1/R_1 -1/R_2 )
Concave lens:
parallel rays go through opposite side focal point
ray through centre is undeviated
ray through incident side focal point is refracted parallel to axis
Convex lens:
parallel ray appears to have come from F_1
rays through the centre are undeviated
rays through F_1  emerge parallel to the axis
Cameras:
f_number=f/D
1185 for eye diagram
Myopia fixed with diverging lens
Hyperopia fixed with converging lens

[bjornredtail]

How about a packet-radio link to a team of folks with Internet Connections?

And why, yes, I am a fake Engineer. Computer science does not count in the slightest.

[windhound]

...or just a local lan
All of our campus buildings are blanketed in wifi, I'm not sure how turn-off-able it is...  not very I suspect, as you'd have to kill off the common area, study rooms, and computer lab's wifi as well or risk leaching.  It wouldn't be a popular choice.  Easier to just forbade laptops or anything that can carry a wireless signal.

But yeah, Comp Sci isnt really fake engineering.  Engineering be hardware.  Ye be software.
It is kinda interesting though, in my "Advanced Microprocessor Design" class the professor occasionally mentions there's a software way to handle this function, then proceeds to explain the hardware method.  I'm guessing programming at the hardware level is a branch of comp sci, or maybe CpE grad students get more into it

Rather impressive sheet Shadow, wiiide range.  Assuming its for your final?  I mean, from capacitance to convex lenses...

...
on a side note, firefox pwns
on one hand, it did manage to crash spectacularly
on the other, it restored all my tabs (~30) including my unsubmitted post

[Shadow]

Yeah that'd fpr the final. and I stil have diffraction and interference to add to that. We covered a ridiculous variety of topics in this class.

But yah, I don't know what the internet rules are, and I don't lan on bringing a laptop at all - my formula sheet and textbook will be more helpful.

[Shadow]

List update: 90% done. I'm beginning to wonder if this will be a help or a hindrance in the exam. Microsoft word obviousl isn't very efficient at handling large numbers of formulas, the worksheet is starting to get jumpy and erratic, and it crashed in a vey wierd way on me once. Luckily I save often.


Fluids
ρ=m/V
p_2=p_top+ρgh
Hydraulic press:
F_2=A_2/A_1  F_1
Buoyancy
Force exerted by pressure difference:
F=(p_a-p_i )A
F_buoy=ρ_fluid gV
F_net=F_g (1-ρ_f/ρ_o )
Submerged object:
F_net=(ρ_f-ρ_o ) V_o g
Floating object:
V = volume of object underwater, buoyant force balances weight exactly
V/V_o =ρ_o/ρ_f →the fraction of the object below the surface
Surface tension (F-36)
γ=F/d
p=p_a+4γ/R

Capillary:
h=2γcosθ/ρgr
Fluid flow:
A_1 v_1=A_2 v_2→volume flow rate
A_1 v_1 ρ_1=A_2 v_2 ρ_2→mass flow rate
p_1+ρgh_1+1/2 ρv_1^2=constant

Venturi meter (F44')
v=√(2gh(ρ_fluid-ρ_liquid )/([(A/a)^2-1] ρ_liquid ))→fluid refers to the measuring device,liquid to the moving liquid
Toricelli
v_b=√2gh
Viscosity
η= FL/Av
R_e=ρvd/η→if≥2000,turbulent.If≤2000,laminar.If 2000≤R_e≤3000,unstable.
Thermodynamics
Zeroth Law:
Two bodies in thermal equilibrium with a third are also in equilibrium with each other.
First Law:
Energy is conserved
Second Law:
Entropy always increases or stays the same in spontaneous processes
Third Law:
T_f=9/5 T_c+32→ΔT_f=9/5 ΔT_c
T_c=5/9 (T_f-32)→ΔT_c=5/9 ΔT_f
Thermal expansion:
ΔL=αL_0 ΔT→L=L_0 (1+αΔT)
α=(ΔL/L_0 )/ΔT
β=3α


Calorimetry and heat transfer:
Q=mcΔT
Q=mL_f
H=kA((T_2-T_1)/L)→k=thermal conductivity constant,A=cross-sectional area,L=length of transfer
R=L/k→H=A(T_2-T_1 )/R→R^' s in⁡〖series are summed〗
Interface transfers:
T=(〖(k〗_1 L_2 T_1+k_2 L_1 T_2))/(k_1 L_2+k_2 L_1 )=(R_2 T_1+R_1 T_2)/(R_1+R_2 )
H=A(T_2-T_1 )/(L_2/k_2 +L_1/k_1 )
Radiation:
P=σAeT^4→σ=5.6696*〖10〗^(-8),A=surface area,0≤e≤1,T(K)
P_net=σAe(T^4-T_0^4 )
Gas transformations:
pV=NkT→N=nN_A,k=R/N_A
C_P-C_V=R→C_V=3/2 R for monatomic,5/2 R for diatomic
γ=C_P/C_V =1.40 for diatomic,1.67 for monatomic
ΔU=nC_V ΔT

Adiabatic:
ΔU=-W,Q=0,W=(P_1 V_1-P_2 V_2)/(γ-1)
pV^γ=constant
TV^(γ-1)=constant
Free expansion:
ΔU=0,Q=0,W=0
Isovolumetric:
ΔU=Q=nC_V ΔT ,Q=3/2 nRΔT=nC_V nΔT ,W=0
Isobaric:
ΔU= nC_P ΔT-p(V_f-V_i),Q= nC_p ΔT,W=p(V_f-V_i)
Isothermal:
ΔU=0,Q=W,W=nRTln(V_f/V_i )
Microscopic Interpretations of pressure:
p=(2/3)(N/V)(1/2 mv^2 )
T=(2/3k)(1/2 mv^2 )
K_kinetic=1/2 kT per degree of freedom
E=f/2 nRT=f/2 NkT=N(1/2 mv^2 )→f=degree of freedom,3 for mono,5 for dia.
v_rms=√(3RT/M)  M=molar mass,carefulof units
v_avg=√(8RT/πM)→average speed,used in all above equations
v_p=√(2RT/M)→most probable speed
f=√2 πd^2 v_avg (N/V)→frequncy of collisions
λ=1/(√2 πd^2 (N/V) )→average free path
N/V=P/kT=(PN_A)/RT
s_avg=1/(N/V)^((1/3) ) →average separation between molecules
Avogadro's equation can be found on Q-57a
Heat engines
Cyclic process means Q=W
Q=W=Q_h-Q_c
e=W/Q_h =1-Q_c/Q_h →heat engine
K_r=Q_c/W=Q_c/(Q_h-Q_c )→refrigerator
Carnot cycle:
Q_c/Q_h =T_c/T_h
K_C=T_c/(T_h-T_c )
e_c=1-T_c/T_h
Otto cycle:
e_o=1-(V_2/V_1 )^(γ-1)=1-T_A/T_B =1-T_D/T_C
Heat pump:
K_HP=Q_H/W=Q_h/(Q_h-Q_c )<T_h/(T_h-T_c )
Entropy:
S=∫_i^f▒dQ/T  (see page Q92+)
dQ=nC_V dT+nRTdV/V
dQ=mcdT→ΔS=mcln(T_F/T_i )
Free expansion:
ΔS=nRTln(V_F/V_i )
W_unavailable=T_c ΔS_universe
ΔS=kNln(V_f/V_i )
W=V_i/V_m →V_m=volume of a molecule
S=klnW where W=W_f/W_i
Electricity:
e=1.60219*〖10〗^(-19)C
mass of e=9.1*〖10〗^(-21)
k=8.9875*〖10〗^9
ϵ_0=8.8542*〖10〗^(-12)
Electric field lines start on positive charges and end on negative ones.
F=(kq_1 q_2)/r^2
E=kq/r^2
Dipoles:
p=2aq      where 2a is the distance separating charges and p points from-to+
τ=p x E=pEsinθ
W=pE(-cosθ+cos⁡〖θ_0 〗)
U=-p x E
Motion in an electric field:
y=eE/(2mv_0^2 ) x^2
Flux:
ϕ=∮▒〖E*dA〗
ϕ_c=q/ϵ_0    set this equal to surface integral to solve for E
Pages E36 + p772 for many examples.
Dipoles:
p=qd and point in direction from negative to positive charge
τ=pEsinϕ=qdEsinϕ=p x E
U(ϕ)= -p*E= -pEcosϕ
W=pEcosϕ_2-pEcosϕ_1
Electric potential:
F=(kq_1 q_2)/r^2
U=(kq_1 q_2)/r
U=k∑_(i<j)^n▒(q_i q_j)/r_ij
ΔU=〖-q〗_0 ∫_i^f▒〖E*ds〗
ΔV=-∫_i^f▒〖E*ds〗 
V=kq/r   for point charge
V=k∑_i▒q_i/r_i =k∫▒dq/r
Capacitance
C=Q/V_ab
Capacitance depends on geometry, proportional to area and inversely proportional to the distance between the plates.
C=(ϵ_0 A)/d  for parallel plate capacitor
In series, the magnitude of the charges is the same on each capacitor:
1/C_eq = ∑_(i=1)^n▒1/C_i
V_eq= ∑_(i=1)^n▒V_i
In parallel, the voltage difference is the same across each capacitor:
C_eq=∑_(i=1)^n▒C_i
Q_eq=∑_(i=1)^n▒Q_i
Potential energy in a capacitor:
U=Q^2/2C=1/2 CV^2=1/2 QV


Energy density in vacuum:
u=1/2 ϵ_0 E^2
Dielectrics:
K=C/C_0
V=V_0/K
E=E_0/K
σ_i=σ(1-1/K)   indiuced surface charge density
ϵ=Kϵ_0   is the permittivity
u=1/2 ϵE^2  and more on page 830
∮▒〖KE*dA=Q_enc/ϵ_0 〗
Work is the area under the Q-V curve. pE79'
Current and Resistance:
I=n|q| v_d A    where n is the particle density m^(-3)
J=n|q| v_d  is the current density   J=I/A
n=ρ(kq/m^3 )/M(kg/mole) *N_A
ρ=E/J    definition of resistivity
ρ(T)= ρ_0 (1+α(T-T_0 ) )
Page 852 for alpha values.
R=ρL/A
V=IR
R(T)= R_0 (1+α(T-T_0 ) )     ΔR=R_0 αΔT

EMF: ϵ=voltage of EMF source
ϵ=V_ab=IR   in ideal EMF sources
V_ab=ϵ-Ir      for sources with internal resistance
V_ab=IR
I=ϵ/(R+r)       R+r=total circuit resistance
P=V_ab I=I^2 R=(V_ab^2)/R    power input to a resistor
P=ϵI-I^2 r    power output of  source
Iϵ=I^2 R+I^2 r
P=ϵI+I^2 R   power input to a source
Metallic conductivity:
v_av=v_d= aτ=qτE/m    where m is mass and τ is the average time between collisions
J=(nq^2 τE)/m=σE
ρ=m/(nq^2 τ)  for resistivity,and conductivity is the reciprocal
In series:
R_eq= ∑_(i=1)^n▒R_i
I=I_1=I_2...=I_n
V_eq= ∑_(i=1)^n▒V_i

In parallel:
1/R_eq = ∑_(i=1)^n▒1/R_i
V=V_1=V_2=V_n
I_eq= ∑_(i=1)^n▒I_i
DC Circuits:
Ammeters have 0 resistance (p892)
I_fullscale R_coil=(I_new-I_fullscale ) R_shunt   
where fullscale is the initial max and new is the desired max, shunt is the shunt resistance and coil the internal ammeter resistance.
Voltmeters have infinite reistence
V_V=I_fs (R_c+ R_s )
Where V is the max possible and the max without the added resistor s is just IR.
More on page E-116.
Charging capacitors:
q=Cϵ(1-e^(-t/RC) )     where Cϵ=Q
i=I_0 e^(-t/RC)     where I_0=ϵ/R
τ=RC is the time constant
Discharging capacitors:
q=Q_0 e^(-t/RC)
i=I_0 e^(-t/RC)
Galvanometer:
NIAB=κΦ  where N=number of loops,A=area of loops,B=magnetic field,κ=torsion constant,Φ=angular displacement and I=current
Light:
c=2.9979*〖10〗^8  m/s
n=c/v
θ_i=θ_r  for plane mirrors
n_1 sinθ_1=n_2 sinθ_2
λ=λ_0/n
sinθ_crit=n_b/n_a   for n_b>n_a  and n_b  the index of the resultant medium
Polarization:
I=I_0/2  for unpolarized light becoming polarized
I=I_0  cos^2⁡θ for polarised light passing through an analyzer
tanθ_p=n_b/n_a    reflected light is completely polarized perpendicular to the plane of incidence
For θ_p the reflected and refracted beams are perpendicular and the refracted beam is partially polarized parallel to the plane of incidence.
I_blue/I_red ≈ 9.4   
I ~ 1/λ^4   light is most strongly polarized if it is seen perpendicular to it path of travel
Geometric optics:
Sign conventions:
s>0 if object is on incoming light side.
s^' is positive if it is on the opposite side as s
C>0 if C is on the outgoing light side of the surface (positive for concave, negative for convex, see pg 1611)
m=y^'/y=-s^'/s  if m<0,image in inverted

Spherical reflective surfaces:
any ray passing through C is reflected back on itself
any ray passsing through f is reflected parallel and any parallel ray is reflected through f
any ray to the vertex reflects symmetrically around optic axis
1/s+1/s^' =2/R=1/f
Refraction at spherical interface:
n_a/s+n_b/s^' =(n_b-n_a)/R
m=y^'/y=-(n_a s^')/(n_b s)
for convex refracting surface,R>0 since it is on the same side as outoign rays,see 1171.
Thin lenses:
1/s+1/s^' =1/f
m=-s^'/s
See 1176 for various names of lens combinations
1/f=(n-1)(1/R_1 -1/R_2 )
Concave lens:
parallel rays go through opposite side focal point
ray through centre is undeviated
ray through incident side focal point is refracted parallel to axis
Convex lens:
parallel ray appears to have come from F_1
rays through the centre are undeviated
rays through F_1  emerge parallel to the axis
Cameras:
f_number=f/D
1185 for eye diagram
Myopia fixed with diverging lens
Hyperopia fixed with converging lens
power=1/f  m^(-1)
Magnifier allows an object to be placed closer than the nearpoint, and if the focal point is at the near point, the image will be enlarged and virtual and formed at infinity.
M=θ^'/θ    θ=y/25cm and θ^'=y/f  so M is 25cm/f  for simple magnifier
M_combo=M_1 M_2=(25s_1^')/(f_objective f_eyepiece )  for compound microscope (all in cm)  final image inverted.
M_telescope= -f_objective/f_eyepiece   inverted image
1196 for sign rules summary
Interference:
Double slit:
dsinθ=mλ  (constructive)
dsinθ=(m+1/2)λ  (destructive)
y_m=Rmλ/d  where y is the distance from centre to m constructive band and R is the distance from slit to screen
For larger angles:
y_m=Rtanθ_m
Amplitude:
E_p=2E|cos⁡(ϕ/2) |  where ϕis phase difference
I=S_av=(E_p^2)/(2μ_0 c)=1/2 √(ϵ_0/μ_0 ) E_p^2=1/2 ϵ_0 cE_p^2=2ϵ_0 cE^2  cos^2⁡(ϕ/2)  which maxes at ϕ=0
μ_0=1/(ϵ_0 c^2 )
I=I_0  cos^2⁡(ϕ/2)
ϕ=2π/λ (r_2-r_1 )=2πd/λ sinθ   k=2π/λ    k=nk_0  for material changes
I=I_0  cos^2⁡〖(1/2 kdsinθ)=I_0  cos^2⁡〖(πd/λ sinθ)=I_0  cos^2⁡〖(kdy/2R)=I_0  cos^2⁡(πdy/λR) 〗 〗 〗
Thin film interference:
E_R=(n_a-n_b)/(n_a+n_b ) E_i
if n_a>n_b  there is no phase shift
if n_a=n_b,why is this even a case?
if n_a<n_b  there is a phase shift of 180°=πrad
If there is no relative phase change:
2t=mλ/n    (constructive)   where n is the index of refraction in the gap
2t=(m+1/2)λ/n  destructive
If there is a phase change in only one, they are reversed. 1220.
x=mlλ/2h    where x is the distance between inteference fringes
Darkness at contact point for phase change in one, brightness at contact for no relative phase change.

1/4 (λ/n)   for nonreflective coating where n in the index of the coating 1/2 for reflective coating



Single slit diffraction:
sinθ=mλ/a=θ for small angles (destructive)
y_m=xmλ/a   for y≪x and x the distance from slit to screen
I=I_0 [sin⁡(β/2)/(β/2)]^2   where   β=2π/λ asinθ       so I=I_0 {sin⁡[πa(sinθ)/λ]/(πa sinθ/λ)}^2
β≅±(2m+1)π   (constructive)
I_m≅I_0/((m+1/2)^2 π^2 )    for 〖max 〗⁡intensities
Double slit, finite slit width:
I=I_0  cos^2⁡〖(ϕ/2) [sin⁡(β/2)/(β/2)]^2   where β=2πa/λ sinθ 〗    and ϕ=2πd/λ sinθ  see page 1244 for details
if dsinθ=m_i λ   and asinθ=m_d λ,solving for m_i and m_d  give missing maximums
Several slits:
dsinθ=mλ (constructive)
Resolution of a spectrograph:
R=λ/Δλ=(1/2 (λ_1+λ_2 ))/(λ_2-λ_1 )=Nm
X-ray diffraction:
2dsinθ=mλ   (constructive)
Circular apertures:
sinθ_1=1.22λ/D=resolving power (first dark ring)  next two are given by 2.23 and 3.24
bright ring angular radii are sinθ=1.63 ,2.68 ,3.70 (λ/D)
Holography:
r_m=√(2mλb_0 )    where b_0  is distance to film and r_m is distance from centre to max.

[Takara]

*bleep bleep bleep*

We're sorry, but your call cannot go through. Please hang up and try again.

O_o

[Firetooth]

Only physics I know is:
Apple<Orange-F_6^e

[Krowdon]

I dont like Physics. too confusing.