Roman Ya. Kezerashvili

New York City College of Technology, The City University of New York

New York City College of Technology, CUNY

300 Jay Street

Brooklyn, NY 11201

718-260-5277

rkezerashvili@citytech.cuny.edu

Advanced Optics with Laser Pointer and Metersticks

Abstract

We are using a laser pointer as a light source, and metersticks as an optical branch and the screen for wave optics experiments. It is shown the setup for measurements of wavelength of laser light and rating radial spacing of the CD, diffraction on a wire and observation of a hologram.

Construction and Use of Apparatus:

Laser pointers also know as laser penlights, have become very affordable recently due to new developments in laser technology. They are widely available at electronic stores, novelty shops, through mail order catalogs and by numerous other sources. They are in the price range from $1 to $30 as other electronic toys and are being treated as such by many parents and children. Pointers are used for other purposes such as the aligning of other lasers, laying pipes in construction, and as aiming devices for firearms.

Laser pointer can be use to observe the interference, diffraction and polarization of light in college physics laboratory. Laser pointers can be used to produce holograms. There were opinions it couldn't be done because of the short coherence of the beam and that laser pointers were not polarized. But it was practically proved that a laser pointer could be used not only to observe a hologram but also to produce a high quality reflection display hologram.

We suggested a series of experiments with a laser pointer as a light source, and using metersticks as an optical branch and the screen to measure the interference and diffraction patterns. All setups are in range of $65.

· Determination of wavelength of laser Light

A wave phenomenon, which occurs when two or more waves overlap in the same region of space at the same time and form an interference pattern, is known as the interference of waves. When two waves of the same frequency but of different phases combine, the resultant wave is a wave of the same frequency, the amplitude of which depends on the phase difference. If the phase difference is 0 or an integer times 2p, the waves are in phase and interfere constructively. For the constructive interference, the resultant amplitude equals the sum of the individual amplitudes, and the intensity has a maximum. If the phase difference is p or any odd integer times p, the waves are out of phase and interfere destructively. For destructive interference the resultant amplitude is the difference between the individual amplitudes, and the intensity has a minimum. If the two sources have the same amplitude, the destructive interference results in the zero net amplitude. The phase difference between two waves is often the result of difference in path length traveled by the two waves. If waves from two sources with the same wavelength arrive at the same point together with exactly the same phase, then the condition for maximum constructive interference is that the path length of two waves must be identical or else differ by an integer multiple of the wavelength, that is

(constructive interference), (1)

where D₁ and D₂ are the path lengths of the waves from their source to the point P (Fig. 1). If the distances D₁ and D₂ are quite large compared to the separation d between the sources, we can write the conditions for the constructive and destructive interferences in terms of the angle q and the distance of separation d. When the distance d between the light sources and the plane containing the observation point is much greater than L, two paths D₁ and D₂ are nearly parallel and the path difference is approximately , as shown in Fig.1. This result gives equation for determining the constructive interference of the resultant wave at point P:

(constructive interference), (2)

As it is shown in Fig. 1, the distance y_m measured along the screen from the central bright point to the mth bright fringe is related to the angle q by

. (3)

Substituting this into equation (2) we obtain

. (4)

Solving equation (6) for wavelength we get

(constructive interference). (5)

Thus, for the known distance of separation d, by measuring the distance y_m along the screen from the central bright point to each of the mth bright fringe and the distance L from the slit to the screen, we can determine the wavelength of the monochromatic light. We determine the wavelength of the laser light using diffraction grating. In the first part of this experimental activity we will be using a monochromatic laser beam, which is incident normally on a transmission diffraction grating. By observing the interference pattern and measuring the distances y_m between the central bright maximum and each of the mth bright fringe and the distance L from the diffraction grating to the screen, we will determine the wavelength of the laser light from equation (5).

· Determination of the grating radial spacing of the CD

By solving equation (5) for the distance of separation d we obtain

(constructive interference). (6)

Equation (6) allows us to determine the distance of separation between the light sources. That means we can find a grating spacing by using a light source of a known wavelength and measuring the distance y_m along the screen from the central bright point to each of the mth bright fringe and the distance L from the slit to the screen.

The rainbow-colored reflections that you can see from the surface of a CD are the reflection grating effects. The grooves are tiny pits 0.1 mm deep on the surface of the disc, with the uniform radial spacing of d=1.6 mm. The reflection grating aspect of the CD is merely an aesthetic side benefit. The interference pattern produced on the screen on a large distance from the grating is due to a large number of equally spaced light sources. The interference maxima are at the angle q given by equation (3). In this part of the experiment the monochromatic laser beam will incident normally on a reflection diffraction grating. We will be using a CD as the reflection diffraction grating. By measuring the distances y_m between the central bright maximum and each of the mth bright fringe, the distance L from the CD to the screen and using the wavelength of the laser light found previously, we will determine the grating radial spacing of the CD from equation (6).

· Diffraction on a wire

In this experiment a thin wire is inserted in the path of a laser pointer beam and diffracted spots are projected on a meterstick-screen as it is shown in Fig. 4. A general condition for a bright fridge of the diffraction pattern is

(7)

where a is the diameter of wire. The central bright fringe occurring at q=0 and is the brightest, secondary and so on bright fringes occurring on both side of the central maximum. However, the intensity of those maxima diminish more rapidly. From the Fig. 4 we see that for the small angle q we can replace sinq by the expression

(8)

where d_m is the distance between two symmetrical bright fringes of the same order m, and L is a distance between the wire and the meterstick-screen. Substituting equation (8) into equation (7) gives the diameter of the wire as

Therefore, we can find the diameter of the thin wire by measuring the distances between two symmetrical bright fringes of the same order m, and the distance L. In this experiment using a laser pointer you can observe the sharp diffraction pattern for the wire of the gages from 34 to 48 ( 0.16 -0.03 mm).

· Observation of a Hologram

One of the most familiar applications of laser is a process for producing three-dimensional images. To produce a holographic image, the laser beam from the laser pointer passes through the center of the diverging lens (from -6mm to -25mm focal length, double concave lens) which spreads the beam to uniformly illuminated the transparent hologram .The basic setup for a single beam transmission hologram is shown in Fig. 5. The distance between the diverging lens and the hologram holder is approximately 1 m (the distance depends on the focal length of the diverging lens) to get uniform illumination.

Equipment and costs required to construct apparatus:

Interference and CD Experiment

Item	Source	Part number	Cost
Laser pointer	Any store		$7
Meterstick	Sargent-Welch	WLS-44696	$5.40 set/2
Meterstick Holders	Sargent-Welch	WLS-3602A	$3.50 set/2
Holders	Sargent-Welch	CP86255-00	$20
Diffraction grading	Amer. 3B Scientific	CP-U21872	$8.25
Total Cost			$53.05

Equipment and costs required to construct apparatus: Diffraction on wire

Item	Source	Part number	Cost
Laser pointer	Any store		$7
Meterstick	Sargent-Welch	WLS-44696	$5.40 set/2
Meterstick Holders	Sargent-Welch	WLS-3602A	$3.50 set/2
Holders	Sargent-Welch	CP86255-00	$20
Total Cost			$61.80

Equipment and costs required to construct apparatus: Observation of Hologram

Item	Source	Part number	Cost
Laser pointer	Any store		$7
Meterstick	Sargent-Welch	WLS-44696	$5.40
Meterstick Holders	Sargent-Welch	WLS-3602A	$3.50 set/2
Holder	Sargent-Welch	CP86255-00	$20
Diverging lens			$10
Hologram	Pasco	OS-9115	$29
Total Cost			$78.40