Using the Naked Eye to Analyze Polarized Light From a Smartphone

Human polarization perception provides no known biological or behavioral advantage; nevertheless, the human eye, like the eyes of many animals, is sensitive to the polarization of light.^2,3 We can detect the angle of plane polarized light using an entoptic phenomenon called Haidinger’s brush, named after the Austrian scientist Wilhelm Haidinger, who first reported it in 1844.⁴ It originates inside the eye and does not correspond to any real object. As such, it cannot be photographed.

To see Haidinger’s brush, look at a large white or blue area on an LCD screen, for example, a smartphone.⁵ We provide a free app for that purpose.⁶ Then, slowly tilt the head or rotate the screen. Now an image appears centered on the fixation point (Fig. 1). We will later explain why the image is not a real image on the layer of the screen.

If, at first, one cannot see Haidinger’s brush, one should not be discouraged as it gets easier to see with training. However, one must manage certain constraints, as follows. For example, eyeglasses with plastic lenses as well as protective films placed over the screen may disrupt the linear polarization. OLED displays may not be usable (cf. appendix⁷). For these reasons, teachers should consider testing the polarization of students’ smartphones. Eventually, students can share their smartphones for the activity in class. As an alternative, one could also use LCD computer screens.⁵ 

If the plane of polarization relative to the eye does not change, the effect will vanish after about two seconds. When the polarization of the light is rapidly switched in front of the eye, however, the patterns are rapidly reactivated. In the case of white light, the blue brush of the pattern (often not visible) is parallel to the oscillating electric field of the linearly polarized light entering the pupil; the yellow brush is parallel to the oscillation of the magnetic field.

Haidinger’s brush is most easily perceived when blue polarized light is used. Here the brush pattern appears as two perpendicular crossed hourglass-shaped figures, one brighter and one darker than the background. It may also be helpful to dim or turn off the room lights. Visibility may be further improved by rotating the plane of polarization, which results in rotation of the pattern.⁸ For this purpose, simply rotate the smartphone screen at about one rotation per second using a small turntable, e.g., a potter’s wheel or a swivel stand for bar magnets (Fig. 2). Haidinger’s brushes are apparent as a small rotating airplane propeller.

The size of the brushes varies directly with the viewing distance, being smallest when observed at close range, and larger as the viewing distance increases. At a distance of one arm’s length, the brushes are only a few centimeters in size (the illustrations in Figs. 1, 5, and 6 are adjusted for better visibility in print). The exact mechanism of human polarization perception is unknown and is still a topic of research; however, some explanations have been proposed.³ 

Many polymer films rotate the plane of polarization because they have been stretched during manufacturing and are therefore birefringent. As such, the index of refraction is dependent on the direction of polarization (see appendix⁷).⁹ 

When a sheet of common cellophane (which is used for packaging for many products, and is thus easily available and inexpensive) is put between the eye and the screen, the brush will be seen rotated. If the optical path length equals λ/2 of the incident light, then under constant rotation of the linear polarized light source the direction of rotation of Haidinger’s brush flips in an impressive manner.

Certain substances, e.g., sugars, also rotate the plane of polarized light (optical activity). By measuring the angle of rotation, the concentration of the substance in a solution is determined. Conversely, knowing the concentration can lead us back to identifying the substance. Figure 3 shows the measurement principle using a basic polarimeter.

The overall angle of rotation depends on the wavelength of light used and on the temperature. Therefore, these parameters are usually standardized to 589.3 nm (the Sodium D line) and 20 °C. Table I shows the specific optical rotatory power of some sugars. Some carbohydrates rotate the light polarization clockwise (+) and some counterclockwise (−). The angle of rotation is measured clockwise as perceived by looking through the polarizer to the light source.

Sucrose (table sugar) is very water-soluble (at 20 °C about 2 kg/l), and has a molecule composed of glucose and fructose. Note that in general, a freshly prepared water solution of sugar gradually changes in optical rotatory power (mutarotation). If, for example, crystalline α-D-glucose (dextrose) is dissolved in water, the specific rotation gradually decreases from an initial value of+112° until it reaches an equilibrium value of+52°.

The naked-eye polarimetric experiment is realized by using the linearly polarized blue light source of a smartphone screen (see appendix⁷). Look alternately directly on the screen without any sample and through the sugar cell, e.g., by quickly moving the cell back and forth (see Fig. 4).

Note that the type of container holding the sugar solution is very important. It must not disturb the polarization. An optically flat, non-birefringent container is required for these experiments. Those made of plastic could rotate Haidinger’s brushes even without sugar solution. Containers made of glass could have warped surfaces that make the brushes hard to see.

Since the polarization of the light is switched in front of the eye, Haidinger’s patterns are rapidly reactivated.¹⁰ This allows for differential comparison of the two successive polarization states and thus for rough estimation of the degree of rotation. For dextrogyre sucrose (sugar) solutions (c = 300 g/l) in a 10-cm long cell, we observe about 40° ± 10° optical rotation (Fig. 5). Note that due to the optical rotary dispersion, the specific rotation for blue light is about two times the specific rotation for yellow light.¹¹ Hence, the data listed in Table I only serve as an approximation.

The estimation of precision depends on the effort in repeatedly execution of the measurement. Moreover, precision can be statistically increased by averaging values obtained by successive measurements from different observers.

Polarimetric measurements require a prior assessment of both the minimum concentration and the path length to give observable rotations. For example, optical rotation produced by drinks with a relatively high sugar concentration of about 10% and a path length of 10 cm is less than 10°, too little to be easily appreciated with naked-eye polarimetry.

Instead of moving the cuvette, a sheet of cellophane can be moved into and out of the optical path to make the Haidinger brushes visible in both cases with or without the cuvette.

Haidinger’s brush is formed only on the macula and centered on the fovea. Hence, with normal vision it appears centered on the object of fixation. For subjects who have some problem with their central vision, Haidinger’s brush can appear disrupted or it can appear away from the object of fixation (eccentric fixation).¹² 

Haidinger’s brush can be used to train people to look at objects with their macula. The goal of the training is for the user to learn to look at the test object in such a way that the Haidinger’s brush overlaps with the test object.

We propose the use of a smartphone screen as a polarized blue light source for subjective self-test of eccentric vision. For these purposes, the observer rotates a smartphone with a red dot drawn on its display with a removable marker or with a suitable app.⁶ By focusing with one eye on the dot, the rotating Haidinger’s brush will appear centered on the dot [Fig. 6(a)]. Anyone who does not see Haidinger’s brush clearly on the screen or anyone who sees it off-center even after a bit of practice may have vision problems [Fig. 6(b)]. However, it should be made clear to students that this test is not intended for medical diagnosis.

Polarized light is an important part of science curricula (e.g., polarization in wave optics, Hertzian dipoles in electrodynamics, optical activity and stereochemistry in chemistry), as well as in students’ everyday life (e.g., 3D cinema, polarization filters in photography).¹ Usually, students are introduced to the technical reality that one device is needed to generate polarized light (e.g., polarizer, laser) and another device is needed to perceive the orientation of the polarized light (e.g., analyzer) or to make use of it (e.g., 3D glasses).^13,14 The capacity for the naked human eye to perceive light polarization directly is less often discussed. The eye can act as a differential analyzer and determine the orientation of linear polarized light. As a source of linearly polarized light, students can use smartphones with an LCD screen. Hence, students can perform various experiments easily on their own. Even a qualitative comparison regarding the sugar content of different solutions is feasible with a smartphone as source of polarized light and the naked eye as analyzer.

Our experience has shown that students showed high interest in the topic, especially in the ophthalmological self-test.