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2.71/2.710
Optics
Practice
Exam
3
Spring
‘09
1.
A
thin
biconvex
lens
with
the
same
absolute
curvature
on
both
faces
is
used
in
the
two
imaging
systems
shown
below.
In
the
Frst,
both
object
and
image
are
in
air,
whereas
in
the
second
the
object
is
“immersed”
in
a
material
of
index
n
0
< n
g
,
where
n
g
is
the
index
of
the
glass
used
to
make
the
lens.
Compare
the
two
imaging
systems
in
terms
of
imaging
condition
and
magniFcation.
2.
In
the
conFguration
below,
lenses
L1
and
L2
are
identical
with
focal
length
f
,
and
we
consider
them
to
have
inFnite
aperture.
The
system
is
illuminated
coherently
by
an
onaxis
plane
wave.
1
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Write
an
expression
for
the
Feld
at
x
in
terms
of
the
thin
complex
transparencies
g
1
,g
2
.
(b)
Consider
the
speciFc
case
with
f
=
10cm
and
g
1
,
g
2
deFned
as:
If
λ
= 1
µ
m,
derive
and
sketch
the
intensity
at
the
output
plane
x
.
3.
Example:
OTF
of
the
Zernicke
phase
mask
The
thin
phase
transparency
whose
schematic
is
given
below
is
placed
at
the
±ourier
plane
of
a
unit
magniFcation
telescope
with
focal
length
f
=
10cm.
What
is
the
optical
transfer
function
for
quasimonochromatic
illumination
at
wavelength
λ
= 1
µ
m?
4.
Goodman,
Problem
610
5.
Calculate
and
sketch
the
±ourier
transform
F
(
u
)
of
the
function
x
±
²
³
2
πx
´
³
2
πx
´µ
f
(
x
)
=
sinc
cos
+
cos
b
Λ
1
Λ
2
2
±
²
Assume
that
the
following
condition
holds:
1
1
1
1
1
,
,
b
Λ
1
Λ
2
Λ
1
−
Λ
2
6.
A
very
large
observation
screen
(e.g.,
a
blank
piece
of
paper)
is
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.710 taught by Professor Sebaekoh during the Spring '09 term at MIT.
 Spring '09
 SeBaekOh

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