A beam of light reflected by a material whose index of refraction is greater than that of the material in which it is traveling, changes phase by ½ cycle.
Optical Instruments
Focusing The Eye
The Magnifying Glass
The angular of magnification or magnifying power, M, of the lens is defined as the ratio of the angle subtended by an object when using the lens, to the angle subtended using the unaided eye with the object at the near point of the eye.
Telescopes
Magnification of Telescope
M=-fo/fe
Limits of Resolution
The ability of, lens to produce distinct images of two point objects very close together is called the resolution of lens.
Lorentz Factor,
2
21
1
cv
Time Dilation
Clocks moving relative to an observer are measured by that observer to run more slowly.
Length Contraction
220 /1 cvLL
Mass and Energy
2mcE
22 cmmcKE o
Early Quantum Theory and Models of the Atom
Energy distributed among the oscillating electric charges of the molecules is not continuous, but instead consists of a finite number of very small discrete amount, each related to the frequency of oscillation as:
sJh
hfE
34
min
106.6
;
Planck’s Quantum Hypothesis
Planck’s assumption suggests that the energy of any molecular vibration could be only some whole number multiple of hf:
....3,2,1
;min
n
nhfE
Photoelectric Effect
De Broglie Wavelength
mv
h
The Bohr Model
Allowed Angular Momenta
2
hnLn
Allowed Radii
0
22
2
1
1
2
4
1
;4
k
mke
hr
rZ
nrn
Energy Levels of Atom
22
422 12
nh
eZEn
Bohr’s Third Postulate
A single photon is emitted whenever an electron jumps down from one orbit to another.
lowerupper EEhf
Quantum Mechanics of Atoms
The Heisenberg Uncertainty Principle
sJ
hpx
341006.1
2
Quantum Mechanical View of Atoms
Quantum Mechanics of the Hydrogen Atom
n – principal quantum number, positive integer;
l – orbital quantum number, is related to the magnitude of the angular momentum of the electron; at given n can take integer values from 0 to (n-1);
ml – magnetic quantum number, is related to the direction of the electron’s angular momentum, and it can take an integer values from –l to +l.
Complex Atoms and Periodic Table of Elements
Structure and Properties of the Nucleus
Nuclear Radii
3/115 )102.1( Amr
Atomic Mass Unit
227 /5.931106605.11 cMeVkgu
Binding Energy and Nuclear Forces
The total mass of a stable nucleus is always less than the sum of the masses of its constituent protons and neutrons.
Radioactivity
Alpha Decay
Q-Value
The energy released is called the disintegration energy, Q or Q-value:
2)( cMMMQ DP
Beta Decay
Gamma Decay
Half-Life and Rate of Decay
The number of decays N that occur in a very short time interval t is proportional to t and the total number N of radioactive nuclei present: