Lab 4

daughterduckUrban and Civil

Nov 15, 2013 (3 years and 7 months ago)

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Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set


Imaging with a single lens



Aperture and its effect on depth of field



Measuring the focal length with the “auto
-
collimation” method



Spherical Aberration and the Foucault knife test



Total internal reflection: Determining the index of refraction of a liquid
with “Abbes Method”.



Building a beam expander.



Topics

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

Quantity

Sign

+

-

s
o


Real object

Virtual object

s
i

Real image

Virtual image

f

Converging lens

Diverging lens

y
o

Erect object

Inverted object

y
i

Erect image

Inverted image

F
o

F
i

f

x
o

s
o

f

s
i

x
i

y
o

y
i

Thin Lens

f
s
s
i
1
1
1
:
formula

Lens
0


o
i
o
i
T
y
y
s
s
M




:
ion
Magnificat

Transverse
Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.A Imaging by a single lens

Lens

Screen

o
s
i
s
Lens

Screen

o
s
i
s
Figure out the exact position of the filament!

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.B Depth of Field

Depth of field in photograph:



The range of distances over which the image is sharp.



Can be controlled with aperture.



Depth of field is a trade
-
off for time of exposure in
photography:


Smaller aperture = greater depth of field but requires longer exposure
time.


Larger aperture = less depth of field but requires less exposure time.

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

Screen placed away
from image plane:
Blurry image

F
o

F
i

f

x
o

s
o

f

s
i

x
i

y
o

y
i

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

Screen placed away
from image plane but
using an aperture…..

F
o

F
i

f

x
o

s
o

f

s
i

x
i

y
o

y
i

Aperture

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.C Auto
-
collimation method

Lens

Mirror

f
Aperture

Make sure the image appearing here is a
sharp image of the aperture, NOT an
image of the filament!

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Spherical aberration

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Foucault knife test explained

Note: The different colors used are just for the purpose of easier visual tracking.
They do not represent different colors. Assume all rays have the same color.

1

1

2

2

3

3

4

5

6

4

5

6

Perfect Lens

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Foucault knife test explained

Foucault “knife” at position 1 (in front of focus)

1

1

2

2

3

3

4

5

6

4

5

6

Perfect Lens

Screen

Screen

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Foucault knife test explained

Foucault “knife” at position 2 (at focus)

1

1

2

2

3

3

4

5

6

4

5

6

Perfect Lens

Screen

Screen

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Foucault knife test explained

Foucault “knife” at position 3 (behind the focus)

1

1

2

2

3

3

4

5

6

4

5

6

Perfect Lens

Screen

Screen

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Foucault knife test explained

In this example of a lens with spherical aberration, we assume for simplicity two
different focal points: One for “outer rays” (1,6) and one for “inner rays” (2,3,4,5)

1

1

2

2

3

3

4

5

6

4

5

6

Lens with
spherical
aberration

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Foucault knife test explained

1

2

3

4

5

6

Lens with
spherical
aberration

Foucault “knife” at position 1 (in front of “inner” focus)

Screen

Screen

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Foucault knife test explained

1

2

3

4

5

6

Lens with
spherical
aberration

Foucault “knife” at position 2 (in front of “inner” focus)

Screen

Screen

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Foucault knife test explained

1

2

3

4

5

6

Lens with
spherical
aberration

Foucault “knife” at position 3 (between “inner” and “outer” focus)

Screen

Screen

This should be
enough instruction for
you to complete!

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.D Setting up your Foucault knife test

Light Source

Short ends towards each other

18mm lens

Razor blade

Screen

Razor blade

View from the front

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Total internal reflection

critical

1
n
1
2
n
n

1
n
1
2
n
n

critical
n
n
n
n



sin
90
sin
sin
sin

:
Law

s
Snell'
2
1
2
2
1
1




2
1
sin
n
n
critical



Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Determine the refractive index of prism by measuring the critical angle


prism
n
1

n

45
Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Determine the refractive index of prism by measuring the critical angle

critical

prism
n
1

n
Note:

We call the angle on the left the “critical angle” here. That is a bit
different notation compared to the previous example of critical angle.

Task:

Derive the relationship between n
prism

and
Q
critical
.


45
Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Careful when deriving
n
prism

(
Q
critical
): There are two possibilities requiring
you to count the critical angle positive or negative


critical

prism
n




Case A

critical

prism
n




Case B

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E The result will be (please derive):


A

case
for
0

and




B

case
for
0
where
2




critical
critical
critical
prism
n



Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Measuring the critical angle



Use the angular translator and position prism such that the laser hits the prism exactly
at the rotational axis of the rotation stage.


Reorient prism such that when the rotation stage is at 0 degrees the laser light is
back
-
reflected (make sure back
-
reflection goes back into laser).


Use the screen on the arm of the rotation stage to vie outgoing light ray.

Top view

Screen

Laser

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Measuring the critical angle



Use the screen on the arm of the rotation stage to vie outgoing light ray.

Top view

Screen

Laser

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Measuring the index of refraction of a liquid using two prisms


critical

prism
n
Before adding the liquid

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Measuring the index of refraction of a liquid using two prisms


critical

prism
n
After adding the liquid

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

new
critica

prism
n

Reorient to find the new critical angle.


Determine n
liquid
from the new critical angle.


Do not assume that the critical angle is “small”.


Use numerical value of n
prism

from the previous result.


Derive in “steps”:


Knowing n
prism
and the new critical angle, calculate


using Snell’s law.


Calculate


from trigonometric relationship.


Calculate n
liquid

from n
prism

and



using Snell’s law.






liquid
n
Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Beam expansion/contraction using a Kepler
style telescope

Objective Lens

Eyepiece Lens

Parallel Light:

Diameter D
in

Parallel Light:

Diameter D
out

How are D
out

, D
in
, f
o

, and f
e

related? Use trigonometry!

e
f
o
f
Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

IV.E Beam expansion/contraction using a Galileo
style telescope

Objective Lens

Eyepiece Lens

Parallel Light:

Diameter D
in

Parallel Light:

Diameter D
out

o
f
.)
(
neg
f
e
e
o
f
f

Modern Optics Lab

Lab 4: First Experiments with the Advanced Optics Set

Advanced Optics Set Components


In the manual called “Advanced Optics Set” on page 3 there is a list of
components. Check to make sure all of them are in your set. Note that most sets
only have one prism. You will need to borrow a second prism from the TA as
needed.


On page 4 of that manual at the bottom, there is a list of “offsets” for each
component.
Example:

Lenses have an offset of 6.5mm. Keep that in mind when
reading out the location using the marker on the component holder.






6.5 mm