KEY EQUATIONS Flashcards
Lateral Magnification
M=y’/y
M magnification
Y’ image height
Y object height
If m>1 Image is magnified
If m<1 Image is demagnified
If m is positive, Image is upright
If m is negative, Image is inverted
Focal length for a spherical mirror:
Half of the radius of curvature for a spherical mirror.
f= 0.5R concave f= -0.5R convex
The mirror equation:
1/s + 1/s’ = 1/f
S distance from object to mirror
S’ distance from Image to mirror
F mirror focal length
m=-s’/s
Lensmakers Equation:
1/f = (n-1)(1/R1 - 1/R2)
f focal length
n Refractive index
R1 Radius of first curvature
R2 Radius of second curvature
If f is positive, converging lens
If f is negative, diverging lens
F-number (light gathering capacity) of a lens:
Focal length/aperture diameter
f/D
Angular magnification for a simple magnifier:
M= theta’/theta= (y/f)/(y/25) = 25cm/f
Overall angular magnification for a microscope:
Lateral magnification*Angular Magnification
25cm*s’/f1f2
Overall magnification for a telescope:
-f1/f2
Numerical Aperture:
=nsinalpha
N refractive index
Alpha angle
Apparent depth can be found using:
Na/s + Nb/s’ = Nb-Na/R
Double slit
Ym=R (mlambda)/d
Amplitude in two source interference
Ep = 2E|cos(phase angle/2)|
Intensity in two source interference
I0cos^2 phase angle/2
Phase difference
2pi/lambda * path difference
Constructive reflection thin film
2t=mlambda
Destructive reflection thin film
2t= (m+0.5) lambda
Constructive reflection thin film with phase shift
2t=(m+0.5) lambda
Destructive reflection thin film with phase shift
2t=m lambda
Gamma
1/SQRT(1- u^2/c^2)
Time dilation
Gamma*proper time
Length contraction
Proper length/gamma
Lorentz coordinate transformations
x’=gamma(x-ut)
t’=gamma(t-ux/c^2)
Doppler effect
f=SQRT(c+u/c-u f0)
Relativistic momentum
P=mv*gamma
Relativistic kinetic energy
(Gamma-1)mc^2
Total energy of a particle
Gammamc^2
Total energy, rest energy, momentum
E^2 = (mc^2)^2 + (pc)^2
Photoelectric effect
eV0=hf - phase angle
Momentum of a photon
P= E/c=hf/c=h/lambda
Brehmsstrahlung
eV=hf=hc/lambda
Compton scattering
Lambda’-lambda= h/mc (1-cosangle)
De Broglie wavelength of a particle
Lambda = h/p = h/mv
De Broglie wavelength of an electron
Lambda = h/p = h/SQRT(2meV)
Energy of an emitted photon
Hf=hc/lambda = Ei-Ef
Quantisation of angular momentum
L=mvr= n h/2pi
Orbital radii in the Bohr model
Rn= epsilon0 n^2h^2/pime^2
Orbital speeds in the Bohr model
Vn = 1/epsilon0 e^2/2nh
Total energies in the Bohr model
Rn = n^2a En= -hcR/n^2 R= me^4/8*epsilon^2*h^3*c
Stefan-Boltzmann for blackbody
I=SBC*T^4
Wein displacement law
LambdaT = 2.910^-3
Planck radiation law
I= (2pihc^2)/[lambda^5(e^(hc/lambdakt) -1)]