Optional Unit VI: Optics
C. Physical Optics

1. Important Phenomena

Key Concepts

A mechanical model with transverse waves passing through vertical and horizontal slits can be used to conceptualize the polarization of light.

A polarizing filter allows only those light waves polarized in one plane to pass through. (Circular polarizing filters are also available.) Most of the remaining light is absorbed by the filter.

Two polarizing filters, oriented with perpendicular axis of polarization, prevent the transmission of light.

Some types of crystals (calcite, tourmaline, etc.) are natural polarizers.

Synthetic polarizing materials (made from herapathite) are used in many different applications. (Several should be discussed.)

Some reflecting surfaces (glass, water, etc.) polarize light. Scattering of sunlight in the atmosphere also causes polarization.

Light undergoes diffraction when passing around sharp edges (or through small openings.)

Due to the short wavelengths of visible light, the diffraction of light is most pronounced when the slit through which the light is passing is narrow, within the same order of magnitude of the wavelength(s).

The diffraction pattern produced by a single slit produces a bright central region (central maximum), followed by dark regions on either side, and progressing to less intense light regions (secondary maxima) which diminish in intensity further from the centre.

The spacing between the dark regions is constant. The width of the central maximum is approximately twice the width of the subsidiary maxima, which are also nearly evenly spaced.

All other things being equal, the overall width of a diffraction pattern is inversely proportional to the slit width.

Young's double slit experiment gave support to the wave theory of light over the corpuscular (particle) theory.

In Young's experiment the two point sources of light were in phase. A series of light and dark bands (interference fringes) were produced in the interference pattern.

Dark bands are regions of destructive interference. Bright bands are regions of constructive interference. Each slit produces a single slit diffraction pattern. These two patterns interfere with each other, producing evenly spaced bright fringes superimposed on the background single slit pattern. All other things being equal, the spacing of bright fringes is inversely proportional to the slit spacing, d.

The path difference is the difference in the distance light travels from each slit to the screen. It can be expressed in wavelengths. The relationship between the wavelength (), the distance between adjacent bright fringes on the screen (), the separation of the slits (d), and the perpendicular distance between the slit and the screen (L), for an interference pattern can be given as:

Alternatively, using the nth nodal line:

where x is the distance from the central maximum to the nth nodal line (minima), measured from the right bisector. (The equation is only accurate if x<<L, so . For example, if L = 5x the error is about 2%.)

Michelson's interferometer used a beam splitter to split a beam of monochromatic light into two separate paths. The path difference could be adjusted, allowing for a noticeable shift in the fringe pattern.

A diffraction grating can be used to produce an interesting interference pattern.

A diffraction grating has a large number of very narrow slits spaced very closely together. The large number of slits narrows the width of the interference maxima (bright fringes) to narrow lines. The small slit spacing causes the lines formed to be widely separated. Very narrow slits cause the background diffraction pattern to spread out very wide. All that is visible is the central maximum.

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: polarization, polarizing filter, central maximum, secondary maxima, interference fringes, path difference, interferometer, beam splitter, monochromatic light, diffraction grating.

2. Describe a mechanical model which helps to conceptualize the polarization of light.

3. Give examples of reflecting surfaces which are capable of polarizing light.

4. Explain that scattering in the atmosphere produces polarization.

5. Describe the diffraction pattern produced by a single slit.

6. Explain why the diffraction of light is most pronounced when the slit is narrow, within the same order of magnitude of the wavelength(s).

7. Describe the interference pattern produced by Young's double slit experiment.

8. Suggest why Young's double slit experiment gave support to the wave theory of light.

9. Use the relationship between wavelength, the distance between adjacent nodal lines on the screen, the slit separation, and the perpendicular distance between the slits and the screen to solve problems relating to interference.

10. Explain how Michelson's interferometer produced an interference pattern.

Teaching Suggestions, Activities and Demonstrations

1. Formerly, a transverse wave was defined as one in which particles of the medium vibrate at right angles to the direction of motion of the waves. Light waves require no medium, so it is worth having students consider what, if anything, is vibrating

2. Attempt to replicate experimentally the results of Young's double slit experiment.

3. Observe the effects produced when viewing through a single polarizing filter and a pair of polarizing filters.

4. Observe a diffraction pattern produced by light passing through a slit or around a sharp edge.

5. Compare the observed results when viewing a light source through a single slit and a double slit.

6. Perform an activity to observe several different light sources through a diffraction grating.

7. Place a diffraction grating in front of a laser beam. Observe the diffraction pattern that appears on a far wall. (Caution: Never look directly into the light from a laser. Watch for unintended reflections. Mention this important safety precaution to the students.) Using the slit width, the distance to the wall, and any other necessary measurements, determine the wavelength of the laser beam.

   

   Note that with a good diffraction grating, the separation between bright fringes will be in the order of 20⁰. So the assumption made in the double slit formula, that is not valid.

   

   The equation then becomes

   The basic equation for a diffraction grating is

   

8. The experiment can also be performed using an incandescent light source with a straight filament, such as a display-case bulb. Single, double, or multiple slits can be cut on the emulsion side of overexposed 35mm film with razor blades. (Some students taking Industrial Arts may have a good supply of overexposed film.) Painting microscope slides with carbon black can also be done, but this method is messy, and the time spent darkening slides is perhaps better spent doing the experiment and analyzing the results.