Some Lecture Demonstrations for a Course in Experimental Physics

A. Ya. Volkova, N. N. Malov, and A. Ya. Yashkin

1. A Modified Lyubimov Experiment

The well-known Lyubimov experiment with a freely falling pendulum becomes convincing only when the fall is truly free, which is not always possible to achieve; moreover, it requires a tall room.

The following modification of it seems to us more convincing and simpler: on a massive wooden base (Fig. 1) a spring $P$ is fixed, connected to a metal cylinder $C$ ending in a disk-shaped weight $G$. The weight and the cylinder can slide along a vertical guide $H$. When the spring is deformed, they open the contact $K$ in an electric circuit containing several incandescent bulbs $L$ and a cell $E$, mounted on the base $O$. To the prongs $B$ is attached a string suspension, connected at the point $T$ with a long cord passed over a pulley fixed near the ceiling.

Raising the weight with a finger, we first show that when the deformation of the spring is decreased the bulbs light up. Then we slowly raise the apparatus to the ceiling and quickly lower it. The lighting of the bulbs during the descent shows that the deformation of the spring has decreased, and this must be attributed to the reduction of the action of the weight $G$. With proper selection of the spring and the weight, the experiment succeeds at quite low speeds, which makes it possible to carry it out even in single-story lecture halls.

Fig. 1.

2. MODELING THE IONOSPHERE

The fact, mentioned in a physics course, of the reflection of radio waves from the ionosphere is usefully accompanied by showing the following easily performed demonstration: the radiation from a decimeter generator is received by a dipole, behind which, parallel to the generatrices of a parabolic cylinder whose focal line contains the dipole, several daylight lamps (from three to five) are arranged. When the lamps are lit, reception increases considerably (by a factor of 1.5–2), which is the result of reflection of the wave from columns of ionized gas. As a control experiment, it should be shown that lighting the lamps when the generator is not operating does not produce a permanent deflection of the recording instrument connected to the receiving dipole.

3. VACUUM-TUBE GENERATOR OF UNDAMPED OSCILLATIONS

When considering the process of establishing self-oscillations, it is useful to demonstrate this process by means of the following simple experiment: the classical circuit of a vacuum-tube generator (Fig. 2) is supplemented with an electronic commutator \(K\), inductively coupled to the grid and anode circuits, and with a switch \(P\).

Fig. 2.

When the latter is connected to terminals 2, the process of the onset of oscillations is periodically repeated. The vertical plates of oscilloscope \(I\) are connected to points \(a, b\) of the anode circuit; a sawtooth sweep voltage is applied to its horizontal plates. The resulting plane diagram of the oscillatory process is shown in Fig. 3a. To points \(ab\)

and \(ac\) are connected, respectively, to the vertical and horizontal plates of oscilloscope II, on whose screen the phase

Fig. 3a.

Fig. 3b.

diagram of the oscillations is obtained, shown in Fig. 3b; when the switch is set to position 1, undamped oscillations are produced, and the limiting cycle is displayed in the phase plane.

4. INTERFERENCE EXPERIMENT WITH A THIN PLATE

The well-known interference experiment described in Pohl’s book Introduction to Optics, in which an interference pattern is observed, produced by two imaginary light sources in the direction of the straight line \(Oy\) connecting these sources (\(S_1\) and \(S_2\)),

Fig. 4.

makes it possible to obtain a very convincing pattern, accessible for observation by a large audience.

Figure 5 shows a photograph of part of this pattern; its scale can be judged from the wall chart placed in the right-hand corner of the photograph. The pattern is easily obtained when a mercury lamp is used as the light source; the light falls on a mica plate \(50—100\) microns thick, placed at a distance of \(4—5\) meters from the wall on which the pattern is observed. The experiment is so effective that it should be performed at the beginning of the study of interference. At the same time, of course, it is not yet possible to speak of lines of equal inclination, and one has to give an approximate explanation of the phenomenon. In Pohl’s book the possibility of using here a broad source of light is justified in detail—

...but it is not explained why the distance between the interference fringes turns out to be much greater than when observing in the perpendicular direction \(Ox\) (Fig. 4).

Treating the interference pattern as the result of the superposition of two waves from point sources and taking into account the considerable distance of the screen, one may assume that the directions toward the minima of light coincide with the directions of the asymptotes to the hyperbola corresponding to a given path difference. Let the distance between the imaginary sources be \(2c = m_0 \lambda\); the fringe under consideration is characterized by the path difference \(2a = k \lambda\); then for the imaginary semiaxis of the hyperbola we have

Fig. 5.

\[ 2b = \lambda \sqrt{m_0^2 - k^2}. \]

The direction of the asymptote is determined by the expression

\[ \tg \varphi = \frac{b}{a} = \sqrt{\left(\frac{m_0}{k}\right)^2 - 1}. \]

When observing in the direction \(Ox\), the “width of the pattern” corresponding to the path difference \(k = \Delta \ll m_0\) is equal to:

\[ y_0 \simeq D \frac{\Delta}{m_0}. \]

If, however, one observes in the direction \(Oy\), then for the same path difference (in comparison with the greatest path difference \(m_0\)) the pattern has the width

\[ x_0 = D \sqrt{\left(\frac{m_0}{m_0 - \Delta}\right)^2 - 1} \simeq D \sqrt{\frac{2\Delta}{m_0}}. \]

For not too small values of $m_0$, readily attainable with the aid of a mica plate, the difference in the width of the two patterns is quite considerable. The approximate treatment presented seems acceptable to us, since in passing to a more exact treatment (from the point of view of curves of equal thickness) the physical understanding of the phenomenon will be deepened, but the quantitative relations will remain the same (it should be taken into account that the imaginary sources in our case oscillate in opposite phases).