Mark F. Masters and Timothy T. GroveIndiana University-Purdue University Fort Wayne

Fort Wayne IN 46805 USA

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?

Answer-making: given object distance d, and focal length of lens f, where is the image located?

Equivalently: if a plumbdaad is 0.413 kerndons, then if I have 7 kerndons, how many plumbdaads?

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?

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)

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”!

Nature of light and Models of light Geometric optics

◦ Ray-tracing, interpreting ray diagrams◦ Traditional geometric derivations◦ Optical systems◦ Aberrations◦ Point and extended sources◦ Mathematical Formalism

Physical Optics◦ Mathematical wave formalism for light and Maxwell’s

equations.◦ Polarization◦ Interference

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:

Conceptual activities, interactive lecture demonstrations

Derivation activities Application activities

Students often misinterpret diagrams of wave, imagining that the amplitude corresponds to spatial extent of the wave.

AB

C

D

ECartoon snapshot of wave traveling to left

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.

PositionPosition

h

s

R

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

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.

Cornea Radius = 8 mm Anterior chamber (AC)

Index= 1.33

Front surface of lens Radius = 10mm relaxed, 6mm tensed

Back surface of lens Radius = 6 mm Index of refraction of lens

Index = 1.45

Vitreous chamber (VC)

Index = 1.33 3.6 mm

7.2 mm

23 mm

AC

VC

Maxwell’s Equations are given below.

1) t

BE

; 2)

t

EJB

; 3)

E

; 4) 0 B

. They are restatements

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) B

Et

. Using equations 2) and 3), the

vector identity 2( )A A 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.

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 x-direction 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?

y

x

Birefringent optic Linear polarizer

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

These materials are available at http://users.ipfw.edu/masters/

We acknowledge the support of the U.S. National Science Foundation.