2.1

Polarization

Imagine the following scenario in an introductory optics class: Teach first the concept of polarization, and then use two pieces of Polaroid to explain polarization in the standard way. But for students to truly understand polarization, ask the following question in an introductory optics class: How many ways can you think of to polarize light? And explain how each method works! For example, if no Polaroid film is available, explain how tourmaline can be used as a polarizer. Explain the Nicol Prism, Foucault’s Prism, Iceland Spar (calcite), Ahren’s Prism, the Glan Prism, the Rochon Prism, a “stacked-glass” polariscope or explain how a polished mahogany table can function as an analyzer. Wright [20] recommends 10-12 glass plates in the stack, with the bottom of the lowest plate blackened, as shown in Figure 1.

Figure 1.

The stacked glass polariscope, reproduced from Ref. [20], Fig. 167. Understanding of this polarizer is slightly more difficult for students than other types of polarizers.

2.2

Birefringence

The use of mica or other minerals such as selenite, which are expensive, can offer interesting hands-on activities to students to demonstrate both thin film interference and birefringence. The idea was beautifully implemented in Ref. [20] but can be reproduced much more easily with two pieces of Polaroid (linear polarizing film). Figure 2 outlines the procedure of a simple experiment. Firstly, a book of muscovite mica can be very easily divided into very thin and transparent leaves. Since mica is birefringent, the method of using crossed polarizers can be used to illustrate a beautiful interference effect. With a single leaf of mica sandwiched between non-crossed polarizers, there is a small effect, but when the polarizers are crossed, an interference pattern resembling thin-film interference is set-up which depends on both the thickness of the film and the birefringence of the sample. This method may be useful in teaching both concepts, and may not be readily understood at first glance. The result from the author may not resemble the beauty of the 1892 work in which a vast assortment of beautiful patterns were designed using only mica sheets, but is fast and easy.

Figure 2.

Experiment by the author: (a) A book of mica with one leaf cut away, (b) the leaf between parallel Polaroid pieces, (c) the leaf between crossed Polaroid pieces (illuminated from behind). (d) A similar setup with a more elaborate design in the 1892 reference [20].

2.3

Talbot Effect

The Talbot Effect was first described in 1836 in Philosophical Magazine [47]; an excellent modern description of the effect (with a 2-dimensional grating) is available by Belin and Tyc [48]. The essence of the effect is that a collimated (or quasi-collimated) beam of monochromatic light shone through a grating with a lateral surface feature size of a will produce self images at periodic distances of 2a²/λ, the Talbot length. Intermediate distances produce beautiful patterns which make the effect interesting in an educational setting.

Although the effect may have been more difficult to observe in the 1800s without a laser, it can be now easily created with a single laser pointer and a pair of binoculars, and any 2D stencil pattern with a reasonably small a to give reasonable Talbot distances for visible light. (However, a should not be too small so as to be similar to the wavelength.)

A simple setup of an experiment to observe the effect is shown in Figure 3 built on an optical breadboard, consisting of a red collimated laser diode, followed by a beam expander (in this case, a Keplerian telescope configuration of two convex lenses), followed by a grating. The beam expander ensures a collimated beam, although it is possible for the setup to still function with a single lens which would cause the beam to diverge, although in that case the Talbot distance will be altered and the Talbot image will be magnified (and less bright). A Nikon D7100 DSLR camera with the lens removed was then used to capture images beyond the grating. The image sensor is 23.5 mm x 15.6 mm in size. These images are labeled with the approximate distances from the grating to the camera image sensor and are shown in the collection of Figure 5 (corresponding to the Figure 3 setup and a collimated beam). The images are low quality compared to those in reference [48] and the binoculars setup—the periphery of the patterns show diffraction (probably due to the size of the grating relative to the expanded beam), and there are beam artifacts caused by the [modal quality of the] laser itself. If the laser would be first filtered to improve the beam, it would look better, but this shows that a very simple setup is useful in educational settings. The images shown in Figure 6 correspond to the setup in Figure 3, but with the lens adjacent to the grating moved inwards to create a diverging beam and a magnified set of images. The images shown in Figure 7 correspond to the setup in Figure 4.

Figure 3.

The beam is first expanded with a 2-lens telescope and then passes through the pattern. (One unit cell of the pattern used is shown to the right, where the red circles are open and the rest is opaque with chromium). The spacing between centers of the hexagonal array illustrated by the arrow is 0.72 mm and the radii of the red openings are 0.10 mm.

Figure 4.

No optical table is necessary and no beam expander is necessary. In this case, a 12x50 binocular half acts as a beam expander.

Figure 5.

Direct observations at the image sensor with approximate distances from the grating marked with an expanded, collimated beam. Exact calculation of the Talbot distance for such a grating is described in detail in [48].

Figure 6.

The diverging beam shows increasing magnification, and an increased distance to the Talbot image.

Figure 7.

The aperture of the binoculars was more than twice the diameter of the expanded beam of the setup in Figure 5 resulting in improved images.