2.71/2.710 Optics
Practice Exam 2 - Solutions
Spring 09
1. What is the Fraunhofer diraction pattern of a 1-D slit of size a?
Slit description (1D):
f (x) = rect
x
a
F(u) = asinc(au)
Fourier transform of slit:
0
Diracted far eld:
0 2 +y 0 2
F
0
ax
0 2
2
2
3.012 PS 8
Issued: 11.18.04
Due: 11.24.04
3.012
Fall 2004
BONDING
1. (35 points) What is the expectation value for the potential energy of an electron in the 1s
ground state of the hydrogen atom ? Derive explicitly and explain all the steps in obtaining
y
3.15 Electrical, Optical, and Magnetic Materials and Devices
Caroline A. Ross
Fall Term, 2006
Exam 1 (3 pages)
Closed book exam. Formulae and data are on the last 2 pages of the exam.
This takes 80 min and there are 80 points total. Be brief in your answe
2.003 Engineering Dynamics
Problem Set 2 Solution
Problem 1: A small box of negligible size slides down a curved path defined by the parabola y =
0.4x2 . When it is at point A(xA=2m, yA=1.6m), the speed of the box is Vbox = 8m/s and the
tangential acceler
2.003 Engineering Dynamics
Problem Set 5
Problem 1:
Use symmetry rules to find a set of principal axes that pass through the center of mass for each
of the rigid bodies in the four figures below. In each case cite the symmetry rule used to obtain
the axes
2.71/2.710 Optics
Practice Exam 2
Spring 09
1. What is the Fraunhofer diraction pattern of a 1-D slit of size a?
2. What is the Fraunhofer diraction pattern of this sinusoidal amplitude grating, where
is the grating period?
x i
1h
f (x) =
1 + cos 2
2
3.
2006 3.15 Exam 1
Problem 1
= 105 s, D = 40cm2 s1
a.
Concentration at x = 0: 1010 /cm2 s
ated carriers.
1
104 /cm
105 s = 109 /cm3 of photogener
Therefore:
p = 1018 + 1049 1018 cm3 at surface
n = 102 + 1049 1090 cm3 at surface
L=
Dt =
40 105 = 2 104 cm
1.033/1.57 Q#2: Elasticity Bounds Conical
Indentation Test
November 14, 2003
MIT 1.033/1.57
Fall 2003
Instructor: Franz-Josef ULM
Instrumented nano-indentation is a new technique in materials science and engineering to
determine material properties at ver
0.4
0.3
3s
0.2
3p
0.1
3d
0
0
5
10
15
20
3.012 PS 9 THERMODYNAMICS SOLUTIONS
Issued: 11.24.04
Due: 12.03.04
3.012
Fall 2004
THERMODYNAMICS
1. Phase separation of a regular solution. Given below is thermodynamic data for an A-B
solid solution that exhibits
2.003 Engineering Dynamics
Problem Set 7Questions with answers to concept questions
Problem 1:
A cart of massM is connected to a dashpot with constant c. A force F(t) acts on the mass,
where the force is given by F (t ) Fo cos( t ) .
a). Use Lagranges equ
3.012 PS 9
Issued: 11.24.04
Due: 12.03.04
3.012
Fall 2004
BONDING
1. (10 points) The variational principle states that for a given Hamiltonian the expectation value
of the energy, calculated on any generic trial wavefunction, will always be larger or equa