The refractive index is an important value that is taken into account in the production of such optical devices as microscopes, refractor telescopes, glasses, eye lenses, etc. This article discusses the measurement of the refractive index of glass.
What is light refraction ?
Before considering the features of the experimental measurement of the refractive index of glass, one should get acquainted with the refraction phenomenon itself. Its essence lies in the fracture of the trajectory of a light ray when it crosses the boundary of transparent media of different nature, for example, air and water. It should be noted that both environments must be transparent to light. Otherwise, refraction will not be observed (only the processes of reflection and absorption of light energy will occur).
Mathematics of the phenomenon of refraction
Refraction along with the reflection of light has been studied by mankind since ancient times, it is enough to recall the names of Ptolemy, Heron of Alexandria and Aristotle. The mathematical law describing this phenomenon is called Snell's law.
At the beginning of the XVII century, a Dutch mathematician by the name of Snell (Snellius) was the first to receive the corresponding mathematical expression, summarizing a lot of experimental data. It is worth noting that a similar expression was also obtained by the Arab mathematician Ibn Sahl in the X century, but no one remembered his work after the dark Middle Ages at the dawn of the New Time.
If we denote the angle between the perpendicular to the interface between the media and the incident narrow beam of light by ฮธ 1 (theta one), and between the same perpendicular and the refracted beam by ฮธ 2 , then we can write the equality:
n 1 * sin (ฮธ 1 ) = n 2 * sin (ฮธ 2 ).
This expression is Snell's aforementioned law. Another law of refraction is often added to it, stating that in the plane formed by the incident and refracted rays, also lies a perpendicular to the interface of the media. The values โโof n 1 and n 2 are called the refractive indices of the 1st and 2nd medium.
Absolute refractive index
This physical quantity shows how much light (electromagnetic wave) slows down when it enters a material medium from a vacuum. Mathematically, this definition can be written as follows:
n = c / v.
Here c is the speed of light propagation in vacuum, v is in the material. Since the value of c is always greater than v, the exponent n for any medium is greater than unity. The optical density of the medium correlates with the value of n. For example, for air n is equal to 1, for water - 1.33, that is, water is an optically denser medium.
The refractive index is determined not only by the nature of the material, but also by the frequency of the electromagnetic wave: the larger it is, the greater n. This dependence in physics is known as dispersion. Blue sky is a prime example of the phenomenon of dispersion of sunlight.
Glass refractive index and its measurement
Glass is a solid, transparent material with an amorphous structure. Industrial production of glass is carried out in the form of a number of varieties. Each of them has its own refractive index, which ranges from 1.5 to 1.9.
The determination of this value for glass is easy to carry out in the laboratory. For this, it is necessary to have a lamp that collects optical glass, a set of apertures, a disk with divisions up to fractions of a degree, and a sample of the glass under study in the form of a half-cylinder.
The experiment is performed in the following sequence:
- The lamp is mounted in the focus of the collecting lens. Then it is turned on and with the help of diaphragms they achieve a narrow light beam.
- The disc with divisions is positioned horizontally behind the lens so that a ray of light passes above its surface through the center.
- They put the glass half-cylinder on the disk so that its flat side surface coincides with the diameter of the disk.
- Turn the disk at different angles and measure the angles of incidence and refraction of the beam.
- They process the measured results using the Snell formula, and assuming that the refractive index of light in air is unity.
The figure below shows two different cases of the position of the half-cylinder on the disk relative to the incident beam.
The left picture corresponds to the refraction "air-glass", the right - "glass-air". It is worth noting that when crossing the boundary of two media through a cylindrical surface, refraction does not occur, since a ray of light falls perpendicular to it (along the radius).
Laser refractive index measurement
This experiment is more difficult than the previous one. For it, it is necessary to use a laser with a known wavelength, a small hole through which the laser beam, a glass plate and a screen will pass. Since the spread of the wavelengths emitted by the laser is not large, the dispersion phenomenon does not affect the measurement results. This is the advantage of this method compared to the previous one.
The principle of operation of the laser method consists in the phenomena of diffraction, total internal reflection of light from the boundary of the plate, and interference of waves on the screen. From the analysis of the diffraction pattern, the refractive index of the glass can be calculated.
Since the thickness of the half-cylinder in the previous measurement method is small, the dispersion of light in it can be neglected. This means that the following conclusion is true: it is better to measure the refractive index of a glass using a simpler method with a white light lamp than using a laser.