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
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 ? Der
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 mi
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 spe
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 e
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
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 = 10
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
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
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 ge