Съдържание

Условие Part 1.1.Polarizers (0,8 т.)Part 1.2.Rulers (1 т.)Part 1.3.Strip (0,8 т.)Part 1.4.Liquid crystal cell (0,9 т.)Отговори Решение

IPhO 2014, Експеримент — Задача 1. Part 1.Qualitative observations!

Оригинал на условието (PDF)Съобщи за грешка

Всички материали от IPhO 2014

Experimental competition. Thursday, 17 July 2014 — Experiment. To see invisible! (20 points) · 17 юли 2014 г. · 3,5 т.

Условие

Experiment. To see invisible! (20 points)

Introduction

Many substances exhibit optical anisotropy resulting in that the refractive index turns out dependent on the direction of light propagation and its polarization. Optical anisotropy can occur even in isotropic media in the presence of mechanical stresses, nonuniform heating or application of external electric fields. The direction in which the light propagates without the birefringent is called the optic axis of a crystal.

Consider a traditional optic scheme of experiments for studying the optical anisotropy (see Fig. 1), which is to be used in this experimental problem.

Optic scheme: a light beam passes polarizer 1 (dashed diagonal O1–O1'), the anisotropic plate P (optical axis P–P', vectors E_ins, E_o, E_e) and polarizer 2 (diagonal O2–O2', vectors E'_o, E'_e), leaving with vector E_2. — Fig. 1. Optic scheme of an experiment for studying the optical anisotropy.

Let a light beam fall onto polarizer 1 whose transmission plane intersects its own plane along the straight line $O_1O_1'$ . After passing polarizer 1 the light beam becomes linearly polarized and its electric field strength vector $\vec{E}_0$ oscillates exactly in the transmission plane of polarizer 1. Then, the light beam falls onto the anisotropic plate $P$ oriented such that its optical axis $PP'$ lies in the plate plane to make the angle $45^{\circ}$ with the transmission plane of polarizer 1. Two kinds of light waves are then generated in the plate $P$ : ordinary $\vec{E}_o$ , polarized perpendicular to the optical axis of the plate, and extraordinary $\vec{E}_e$ , polarized along the optical axis of the plate. Refractive indices for these two waves are different and their difference is denoted as $\Delta n = n_o - n_e$ . This results in the appearance of the phase difference $\Delta\varphi = 2\pi h\Delta n/\lambda$ ( $h$ being the plate thickness, $\lambda$ being the wavelength of the incident light in vacuum) between the two waves on leaving the plate. Therefore, the polarization of the outgoing light beam changes to be elliptically polarized. The light beam then falls onto polarizer 2, whose transmission plane $O_2O_2'$ is perpendicular to the transmission plane of polarizer 1.

A simple derivation shows that the intensity of the light beam transmitted through the plate $P$ and polarizer 2 is determined as

I_2 = kI_0\sin^2\frac{\Delta\varphi}{2}, \qquad (1)

where $I_0$ stands for the light intensity falling onto the plate, $k$ denotes the light transmittance coefficient of the plate $P$ and polarizer 2, and $\Delta\varphi$ designates the phase difference between the ordinary and extraordinary waves after passing the plate $P$ .

In this experiment do not evaluate errors unless asked to do so!

The description of the equipment in Appendix A

Photo: flexible plastic strip clamped on the screen and curved; an arrow points to the left edge of the screen holder on the scale. — Fig. 3B Fixing flexible plastic strip to the screen.

Photo: the whole setup with the multimeter, variable resistor, switch, polarizers, screen with the ruler, laser and photodetector on the optical bench. — Fig. 4B Setup for measuring the transmittance of light through plastic ruler

Photo: filters fixed with a pink clamp on the back side of the polarizer, with the photodetector behind it. — Fig. 5B Mounted filters on the polarizer

Photo: optical bench with the laser, polarizer 1, the LCC in its holder, polarizer 2 and the photodetector, with the multimeter and the power supplies. — Figure 6B Setup for measuring the characteristics of the LCC

Part 1.1.Polarizers (0,8 т.)

1.1 Find the orientation (i.e. which of the diagonals) of the transmission plane of polarizer 1 and polarizer 2. Show these planes in the figure in the Answer Sheet. (0.8 points) [0,8 т.]

Part 1.2.Rulers (1 т.)

In this part of the experiment use light emitting diodes (LED) as a light source.

Fix LED on a stand and connect it to its power supply. Set up both polarizers by their face sides (indicated by numbers 1 and 2) pointing towards the light source. Make sure that the polarizers are crossed, i.e. the light beam cannot pass through them. Block the first polarizer by a sheet of white paper placing it on the face side as shown in Fig.1B in Appendix B.

Place the plastic ruler1between the polarizers. You can move the ruler with your hands.

1.2.1 Find the possible directions of the optical axis in the center of the plastic ruler. Show these directions in the figure on the Answer Sheet. (0.4 points) [0,4 т.]

1.2.2 Determine approximately at what distance along the ruler 1 and along the two rulers stacked together, the phase difference for the blue light changes to $2\pi$ . (0.6 points) [0,6 т.]

Part 1.3.Strip (0,8 т.)

1.3.1 Find the possible directions of the optical axis of the strip. Show qualitatively them in the figure in the Answer Sheet. (0.4 points) [0,4 т.]

Using the clamps fix a long flexible plastic strip on the screen so that the strip edges coincide with the screenedges. The strip should be curved (see Fig. 3B). Place the screen with the strip between the polarizers. Shifting the screen, observe the color change of the strip. Measure $x$ coordinates of strip points on the screen scale, use the left edge of the screen holder as an origin as shown in Figure 3B.

Hereinafter coordinates are measured by the scale in the screen. As a pointer, use the left edge of the holder, which indicated in Fig. 3B by the arrow!

1.3.2 Measure the coordinates of the middle points of two dark bands, the left $x_L$ and the right $x_R$ , visible on the strip. (0.4 points) [0,4 т.]

Part 1.4.Liquid crystal cell (0,9 т.)

Liquid crystal (LC) is a state of matter that is intermediate between the crystalline solid and the amorphous liquid. The orientation of its molecules can be easily aligned and controlled by applying an electrical field. The LC cell exhibits the optical anisotropy phenomenon with two principal refractive indices. The magnitude of this effect depends on the applied AC voltage. The Liquid Crystal Cell (LCC) is composed of two glass plates 1 whose inner surface is coated with a transparent conductive layer 2. Between the plates there is a thin (approximately 10 microns) layer of the solution 3 which is in a liquid crystal state. Leads are soldered to the plates for connecting to the AC power supply.

Place the liquid crystal cell (LCC) between the polarizers. Plug it into its power supply. Varying the voltage across the LCC observe the changing colors of the light transmitted through it.

Liquid crystal cell, front and side views: glass plates 1, transparent conductive layers 2, liquid crystal layer 3 (arrows with numbers).

1.4.1 Find the possible directions of the optical axis of the LCC at zero and maximum voltage applied across it. Show these directions in the figure on the Answer Sheet. $Z$ -axis is directed vertically. (0.6 points) [0,6 т.]

1.4.2 Measure the voltage $U_{cr}$ across the cell at which abrupt, with respect to voltage, reorientation of liquid crystal molecules by $90^{\circ}$ occur. Make sure that multimeter is on AC voltage mode. (0.3 points). [0,3 т.]

Appendix A. Experimental equipment

Appendix A photo: light sources — power supply 6 with switch 6a and leads 6b, laser 5 with ring 5a, leads 5b, screws 5c and 5d, LED 4 with leads 4a and screw 4b.

Appendix A photo: variable resistor 7 with terminals 7a, 7b, 7c and knob 7d (with its circuit symbol), and switch 8 with terminals 8a, 8b.

Optical bench 1with holders:
1a – support for the light source with the screw;
1b – support for the photodetector with the screw;
1c, 1d – stands for the polarizers;
1e – stand for the screen and the liquid crystal cell (LCC).

Appendix A photo: optical bench 1 with holders labelled 1a, 1c, 1e, 1d, 1b.

2a, 2b – polarizers on the stands. There are numbers 1 and 2 on their face sides.
The polarizers should be installed with their face sides towards the light source!
The transmission planes of the polarizers makes the angle $45^{\circ}$ with the horizontal.
3 – the screen with the slit (3a) and the scale (3b)

Appendix A photo: screen 3 with slit 3a and scale 3b, and polarizers 2a and 2b on stands with numbers 1 and 2.

Light sources:
4 – light emitting diode (LED):
4a – leads for the power supply;
4b – fixing screw;
5 – laser:
5a – ring for turning the laser with the scale (scale is not used);
5b – leads for the power supply;
5c – the screw for the beam width adjustment on the front side;
5d – fixing screw;
6 – power supply for light sources:
6a – switch;
6b – leads for light source.
Keep the source operating only while making measurements!
Do not point the laser beam in your or anyone’s eyes, it is very dangerous!

7 – variable resistor:
7a, 7b, 7c – terminals for connection to a circuit
7d – knob for changing resistance.

8 – switch:
8a, 8b – terminals for connection to a circuit;

9a – liquid crystal cell (LCC) 9ain a holder (9b), 9c – lead for connecting to the power supply;
10 – the power supply for LCC:
10a – connector for the LCC;
10b – leads for measuring the output voltage;
10c – knob to adjust the output voltage;
10d – power on/off.
Keep the source operating only while making measurements!

Appendix A photos: liquid crystal cell 9a in holder 9b with lead 9c; power supply 10 for the LCC with connector 10a, leads 10b, knob 10c and switch 10d.

11 – multimeter;
Do not press the HOLD button
11a – register to measure resistance (200 kOhm);
11b – register to measure DC voltage (2V);
11c – register to measure AC voltage (20V);
11d, 11e – connectors for test leads;
11f –power on/off.
If the display multimeter is in a "sleep" mode - double-press power on/off!

Appendix A photo: multimeter 11 with registers 11a, 11b, 11c, power switch 11f and connectors 11d, 11e.

When measuring the resistance with the multimeter, the element must be disconnected with a power supply!

Appendix A photo: plastic rulers 12a and 12b, flexible strip 13 and set of filters 14.

Optical elements to be investigated
12 – plastic rulers:
12a –No. 1 (with the scale from 0 to 14 cm)
12b –No. 2 (with the scale from20 to34cm)
13 – flexible strip;
14 – set of identical filters;
The filters and the strip are provided in a separate envelope!
The plastic rulers and the strip exhibit birefringence, their optical axes lie in their own planes.

Appendix A photo: photodetector with input window 15a, leads 15b and fixing screw 15c.

15 Photodetector (photodiode)
15a - input window;
15b - leads for measuring the output voltage;
15c –fixing screw.

Connecting wires, clamps, paper napkin, a piece of paper.

The liquid crystal cell is composed of two glass plates 1 whose inner surface is coated with a transparent conductive layer 2. Between the plates there is a thin (approximately 10 microns) layer of the solution 3 which is in a liquid crystal state. Leads are soldered to the plates for connecting to the AC power supply. In the absence of voltage long molecules of liquid crystal are oriented parallel to the plates. The direction of molecular orientation coincides with the optical axis of the crystal.

Try not to touch those parts of the optical elements through which the light passes! If necessary, wipe them with a paper napkin!