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( ) U = 1 2 kx 2 = 1 ( ) 2 kA 2 cos � t 2 ( ) K = 1 2 mv 2 = 1 ( ) 2 kA 2 sin � t 2 E = U + K = 1 � � � � t ( ) 2 kA 2 x ( t ) = A cos 2 � � = A cos � t � � � � � � T � I 0 = 10 � 12 W/m 2 = 10 � 16 W/cm 2 I Pain = 10 13 I 0 � � f ' = f 1 + u OBS � (stationary source) � � c � SHM = � kx F � � 1 f ' = f � (stationary observer) � � � k k 1 � u SRC / c � � � SHM = � � = 2 � � � � m m � � 1 ± u OBS � � m � c � T = 2 � f ' = (source and/or obs moving) k � � 1 � u SRC sin � � � � mg sin � � mg � � � � c � � � restoring = � mg � = � mg � � s F waves on a string: � � L L 1 = � 1 f 1 = v v � 1 = 2 L 1 � � = s = L � � 1 2 2 L 1 (displacement = arc on circle of radius R) � n = � 1 L n = L 1 f n = v = n f 1 n , n , � � � n mg k = � � � � L m L T = 2 � � T = 2 � k g ( ) , ( ) ( ) = A cos 2 � f 1 t ( ) = A cos 2 � f 2 t � � y 1 t y 2 t I [ ] = 10log 10 � dB ] � � � � I 0 � f 1 � f 2 � � f 1 + f 2 � � � � � y 1 + y 2 = 2 A cos 2 � � cos 2 � � � t � � t � � � I 0 = reference level � � � � � � � � 2 2 f BEAT = f 1 � f 2 f OSC = f 1 + f 2 2 3(

c = 3 � 10 8 m s � 2 , � 0 = 8.85 � 10 � 12 C 2 N � 1 m � 2 µ 0 = 4 � � 10 � 7 T m A � 1 k = 8.99 � 10 9 N � m 2 / C 2 e = 1.60 � 10 � 19 C , c = f � E = cB n 1 sin � 1 = n 2 sin � 2 B 2 u E = 1 u B = 1 2 � 0 E 2 , u E = u B , µ 0 sin � 2 = n 1 2 sin � 1 c n 2 c MEDIUM = E RMS = E MAX B RMS = B MAX n MEDIUM , 2 2 RMS OR u AVG = B 2 1 + 1 = 1 u AVG = � 0 E 2 RMS µ 0 d O d I f � � B 2 m = � d I � � I = u c = c � 0 E 2 � = c � � � µ 0 d O � � Angular magnification: M = � ' ( ) � t absorption: � p = � U = I area � c c Total internal reflection critical angle: sin � c = n 2 reflection: � p = 2 � U / c n 1 ( ) F AVG = I area Total polarization of reflection (Brewster angle): tan � B = n 2 � p AVG = I AVG n 1 c c � � Doppler effect for EM waves : f ' = f 1 ± u 1 refractive power, diopters = � � f ,meters � � c (u = relative speed, use + for approaching, - for moving apart) f - number = f D I � = I 0 cos 2 � (Malus) Magnifiers: N = near point distance for image viewed at � : M = N f , at near point : M = 1 + N f Spherical mirrors: f = R / 2 , d I N Compound microscope : M TOTAL = 1 + 1 = 1 f OBJ f EYEP d O d I f Telescope : M TOTAL = f OBJ L = f OBJ + f EYEP , m = � d I f EYEP d O -(4,()",456+(-"#(7"17'6+($4##"#,8(1+*'56+(-"#(7"16+28(410149+(-"#()&'1+( (: ; (4,()",456+(4-(4$'*+(4,(41(-#"19("-($4##"#8(1+*'56+(4-(<+=41:(( (: > (4,()",456+(4-(4$'*+(4,(41(-#"19("-($4##"#8(1+*'56+(4-(<+=41:( ?(

1 rad = 57.296 � c = f � c = 3 � 10 8 m s � 2 m electron = 9.11 � 10 � 31 kg, 5.49 � 10 � 4 u, 8.19 � 10 � 14 J, 0.511 MeV h = 6.63 � 10 � 34 J � s = 4.135 � 10 � 15 eV � s ; 1 eV = 1.60 � 10 � 19 J Constructive interference: � � = m � , m = 0,1,2 … 2-slit pattern, slit spacing d , bright fringes: sin � = m � d Fringe position on screen at distance L: y m = L tan � m ( ) Path diff for constructive: � � = m � VACUUM = 2 nt or � � = m � n = 2 t where � n = � VACUUM / n n = film index, t = film thickness, m = integer ( ) for destructive. Use m + 1/ 2 ( ) to � � for a reflection with phase change. Add � / 2 m � Single slit of width W , angle � m to order- m minimum: W = sin � m Rayleigh criterion: � min = 1.22 � D Separation at distance L : y = L tan � min � L � min Angle of m th bright fringe for grating with N lines/unit length : � = sin � mN � t 0 1 � v 2 c 2 � t = 1 � v 2 c 2 L = L 0 mv m 0 p = m = E = mc 2 1 � v 2 c 2 , 1 � v 2 c 2 � � ( ) T f peak = 5.88 � 10 10 s � 1 � K � 1 1 K = m 0 c 2 1 � v 2 c 2 � 1 � � � � � � E = hf = hc � K max = hf � W 0 p = h � K = p 2 h 2 � x � p � h � E � t � h 2 m = 2 m � 2 2 � 2 � @(

� � 1 2 2 � 1 1 � � � = R h 2 ) Z 2 ( � � r n = � n 2 E n = � 13.6 eV � � n 2 � � 4 � 2 mkZe 2 � n 2 R = 1.097 � 10 7 m � 1 � � � � p n = mv n = m 2 � ke 2 1 2 � 1 � E = E f � E i = 13.6 eV � � � � 2 � n i n f � � nh � � = 0,1,2... � max where � max = n � 1; m � = � � , … –1, 0, 1, … � � 1, � ( ) h / 2 � ( ) L = � � + 1 deBroglie : n � n = 2 � r n � E = hf = hc � � n = h h = p n mv n 931.5 MeV/ c 2 = 1 u E = � m c 2 N ( t ) = N 0 e � � t R = N � � = ln 2 T 1/2 A X : Z=number of protons, Z A=number of nucleons, number of neutrons N = A - Z Isotope = same Z, different A alpha decay: Z � Z - 2, A � A - 4. beta-minus or -plus decay: Z � Z + 1 or Z � 1, A = unchanged. hadron = strongly interacting, not fundamental: constituents = quarks quark+antiquark = meson, 3 quarks = baryon lepton = weak interaction, fundamental particle boson = integer spin, carrier of forces ( � ,W ± , Z 0 ) fermion = half-integer spin, matter (eg, electrons, nucleons) A(