Download Formula Sheet for Exam #1

Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
Formula Sheet for Exam #1
Reading and thoroughly familiarizing yourself with this formula sheet is an important part
of, but it is not a substitute for, proper exam preparation. The latter requires, among other
things, that you have re-worked all assigned homework problem sets (PS) and the in-class
quizzes, studied the posted PS solutions, and worked and studied the assigned conceptual
practice (CP) problems, as well as (optionally) some practice test (PT) problems, as posted
on the LON-CAPA homework and on the PHYS1112 examples and homework web pages.
You should consult the syllabus, and in particular review the Class Schedule on the last
syllabus page (posted on the PYS1112 course web site), to find out which topics you should
cover in preparing for this exam.
Wave Propagation and Wave Nature of Light
Periodic Wave Condition:
v = λf =
λ
τ
Index of Refraction (IoR) for electromagnetic waves, definition:
n=
c
v
Doppler Effect:
f0 = f 1 ±
u
v
Reflection and Refraction of a Single Ray
For angle of incidence (Θ1 ), angle of reflection (Θ̄1 ) and angle of refraction (Θ2 ):
Archimedes’ Law of Reflection:
Θ1 = Θ̄1
Snell’s Law of Refraction:
sin(Θ1 )/v1 = sin(Θ2 )/v2
where v1 and v2 are the speeds of wave propagation in the respective media. For electromagnetic waves, this is also written as
Snell’s Law in IoR Form:
n1 sin(Θ1 ) = n2 sin(Θ2 )
where n1 ≡ c/v1 and n2 ≡ c/v2 are the corresponding IoR.
Image Formation and Optical Instruments
1
Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
Image-Object-Relations for a Single Device (Lens or Mirror):
Mirror / Thin Lens Equations:
1
1
1
+ 0 =
d d
f
m≡
,
h0
d0
=−
h
d
where d = object distance, d0 = image distance, h = object height, h0 = image height, f =
focal length, m = lateral magnification.
Focal length for reflection at a curved surface (mirror):
f = R/2
Sign Conventions for Single Device (Lens or Mirror):
d > 0 (real object) if object on ”incoming” side; else d < 0 (virtual object).
d0 > 0 (real image) if image on ”outgoing” side; else d0 < 0 (virtual image).
If m > 0 then image erect (upright) rel. to object; else, if m < 0 then image inverted
(upside-down) rel. to object.
If f > 0 then F on ”incoming” and F 0 on ”outgoing” side; else, if f < 0 then F not
on ”incoming” and F 0 not on ”outgoing” side.
R > 0 if center of spherical surface on ”outgoing” side; else R < 0. (For reflection at a
curved surface only.)
Compound Instrument:
If image by device 1 serves as object for device 2 and L =separation of devices then
d01 + d2 = L,
h2 = h01 ,
m12 ≡ h02 /h1 = m1 × m2 ,
where m12 is total lateral magnification of image by 2 relative to object of 1.
Angular Magnification:
Definition:
|M | = Θe /Θref
where Θe =angle subtended at eye by optical instrument’s final image; and Θref =reference
angle subtended at eye by original object viewed without optical instrument at reference
distance dref
Algebra and Trigonometry
2
az + bz + c = 0
⇒
z=
2
−b ±
√
b2 − 4ac
2a
Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
sin θ =
opp
,
hyp
cos θ =
adj
,
hyp
tan θ =
opp
sin θ
=
adj
cos θ
sin2 θ + cos2 θ = 1
For very small angles θ (with |θ| 90o ):
sin θ ∼
= tan θ ∼
= θ (in radians)
Numerical Data
Acceleration of gravity (on Earth):
Speed of light in vacuum:
Biot-Savart’s constant:
Permittivity of vacuum:
Permeability of Vacuum:
Electron mass:
Proton mass:
c = 3.00 × 108 m/s
k = 8.99 × 109 Nm2 /C2
Coulomb’s constant:
Elementary charge:
g = 9.81m/s2
km ≡
µo
4π
= 1 × 10−7 Tm/A (exact)
o ≡ 1/(4πk) = 8.85 × 10−12 C2 /Nm2
µo ≡ 4πkm = 4π × 10−7 Tm/A (exact)
e = 1.60 × 10−19 C
me = 9.11 × 10−31 kg
mp = 1.67 × 10−27 kg
Other numerical inputs will be provided with each problem statement.
SI numerical prefixes:
y = yocto =10−24 , z = zepto =10−21 , a = atto =10−18 , f = femto =10−15 , p = pico =10−12 ,
n = nano =10−9 , µ= micro =10−6 , m = milli =10−3 , c = centi =10−2 , d = deci =10−1 ,
da = deca =10+1 , h = hecto =10+2 , k = kilo =10+3 , M = Mega =10+6 , G = Giga =10+9 ,
T = Tera =10+12 , P = Peta =10+15 , E = Exa =10+18 , Z = Zetta =10+21 , Y = Yotta =10+24 .
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