Transcript Active learning in intermediate optics through class tutorials and

Mark F. Masters and Timothy T. Grove
Indiana University-Purdue University Fort Wayne
Fort Wayne IN 46805 USA
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Our optics class was a very traditional,
lecture-based, geometric and physical optics
class
Outcome: students went through the motions
of doing optics without understanding.
They parroted what they had seen and heard
We had recently completed a successful
revision of introductory classes and labs to
use interactive engagement.
For students to …
 have greater conceptual understanding of light and
optics
 be able to use optics knowledge to solve complex
problems
 be able to work independently in the laboratory.
Ideal for interactive engagement/active learning
But: intermediate classes have different demands
than introductory classes. How to use Interactive
Engagement in this setting?
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Answer-making: given object distance d, and focal
length of lens f, where is the image located?
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Equivalently: if a plumbdaad is 0.413 kerndons, then if I
have 7 kerndons, how many plumbdaads?
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Two systems consisting of a point source, a lens and a
screen. In each system, the point source is located on
the optic axis 10 cm from the lens which has a focal
length of 15 cm. One of the lenses is a diverging lens
and the other is a converging lens. The lenses are the
same diameter. The screen is located 10 cm away from
each lens. Which system will produce the higher
average irradiance on the screen?
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Students passive in classroom –
listen to a lecture, see particular
derivations for optics, see
worked examples.
Students are nominally active at
home through reading book and
doing homework.
Laboratory exercises
(supposedly)
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Concepts: Students wrestle with the material
both in class and out
Students must engage in sense-making rather
than answer making.
 Community: Students work in peer
groups to help each other learn the
physics (and math).
 Communicate: Group and class discussions
with instructor as facilitator (not an
information source) to assist in building
solutions.
Responsibility: Students are responsible for their
own learning. Instructor can assist, but not
“learn ‘em”!
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Nature of light and Models of light
Geometric optics
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Physical Optics
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Ray-tracing, interpreting ray diagrams
Traditional geometric derivations
Optical systems
Aberrations
Point and extended sources
Mathematical Formalism
◦ Mathematical wave formalism for light and Maxwell’s
equations.
◦ Polarization
◦ Interference
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Have the students understand: waves, ray
diagrams, geometric optics.
Have the students be able to solve complex
optics problems
Have the students be able to understand
derivations: how to do them, what
approximations are made.
There are three distinct types of classroom
activities:
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Conceptual activities, interactive lecture
demonstrations
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Derivation activities
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Application activities
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Students often misinterpret diagrams of
wave, imagining that the amplitude
corresponds to spatial extent of the wave.
B
A
C
D
E
Cartoon snapshot of wave traveling to left
# particles/volume
# particles/volume
Position
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Position
Consider the sound wave shown for two different times
(t=0.3ms). Sketch the waveform at each time and
determine the frequency, wavelength and speed of the
wave.
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h
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s
R
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s’
small
•Students are lead through deriving a
result
•Students have to do the work, figuring
out the math, etc rather than simply see
it performed.
WS 22
23 mm
Cornea
Anterior chamber
(AC)
Front surface of lens
AC
3.6 mm
VC
Back surface of lens
Index of refraction of
lens
Vitreous chamber
(VC)
Radius = 8 mm
Index= 1.33
Radius = 10mm
relaxed, 6mm
tensed
Radius = 6 mm
Index = 1.45
Index = 1.33
7.2 mm
The lens is held under constant tension. When you focus your eye, you relieve that
tension and the lens becomes symmetric. The cornea is really a very thin layer.
Accommodation is our ability to change the focus of our eye. This is done by varying the
lens shape.
1) Calculate the refractive power of the “cornea.” You may want to consider a single
refracting surface. Determine what this would mean for an eye that did not have the
“lens.”
2) Calculate the refractive power of the lens for both the relaxed and tensed situations.
Maxwell’s Equations
are given below.
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B
E
1)   E  
; 2)   B  J  
; 3)   E  ; 4)   B  0 . They are restatements
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t
t
of Faraday’s law of induction, Ampere’s Law, Gauss’s law, and no magnetic monopoles,
respectively.
Suppose we take the curl of equation 1)  E  

  B
 . Using equations 2) and 3), the
t
vector identity     A  (  A)   2 A , and the fact that the free charge density
and the
current density equal zero in free space to find a partial differential equation that describes the
electric field. Once you have found that expression, describe what it means about the electric
field.
y
x
Birefringent optic
Linear polarizer
Imagine that you have a material in which the index of refraction depends upon the polarization of the light.
Suppose that for polarizations in the y-direction the index of refraction is 1.31, while for polarization in the xdirection is 1.30. A beam of 532 nm linearly polarized light is incident upon this optical element. Immediately
following the optical element is a linear polarizer which can be rotated.
Write an expression describing a plane wave traveling in the -z-direction, with a polarization axis 15 degrees
above the x-axis. Write a second expression for the wave after the plane wave has traveled through the optical
element. Explain how you arrived at your second expression.
Make two graphs, one with the optic and one without, of the signal recorded on a detector following the linear
polarizer as the polarizer is rotated through an angle of 2 . Assume that the polarization axis of the linear
polarizer is initially aligned with the y-axis.
Are the graphs different? Why or why not.
What effect does the optical element have on polarized light?
Based on these results, if you wanted to make this optic behave as a ½ wave plate, what angle should you set
the polarization of the incident light?
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We applied active learning approaches in lecture
intermediate optics course
The class uses tutorials and interactive engagement
to develop student understanding and sense-making
capabilities
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These materials are available at
http://users.ipfw.edu/masters/
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We acknowledge the support of the U.S. National
Science Foundation.