Optics is one of the old branches of physics. Since ancient Greece, many philosophers have been interested in the laws of movement and propagation of light in various transparent materials, such as water, glass, diamond and air. This article discusses the phenomenon of refraction of light, focuses on the refractive index of air.
Light beam refraction effect
Each in his life faced hundreds of times with the manifestation of this effect when he looked at the bottom of a pond or at a glass of water with some object placed in it. At the same time, the reservoir seemed not as deep as it actually was, and the objects in the glass of water looked deformed or broken.
The phenomenon of refraction of a light beam is a fracture of its rectilinear trajectory when it intersects the interface of two transparent materials. Summarizing a large amount of these experiments, at the beginning of the XVII century the Dutchman Willebord Snell received a mathematical expression that accurately described this phenomenon. This expression is usually written as follows:
n 1 * sin (θ 1 ) = n 2 * sin (θ 2 ) = const.
Here n 1 , n 2 are the absolute refractive indices of light in the corresponding material, θ 1 and θ 2 are the angles between the incident and refracted rays and the perpendicular to the media interface plane, which is drawn through the point of intersection of the beam and this plane.
This formula is called the law of Snell or Snell-Descartes (it was the Frenchman who wrote it in the form presented, the Dutchman used not sines, but units of length).
In addition to this formula, the phenomenon of refraction is described by another law, which is geometric in nature. It consists in the fact that the marked perpendicular to the plane and two rays (refracted and incident) lie in the same plane.
Absolute refractive index
This value is included in Snell's formula, and its value plays an important role. Mathematically, the refractive index n corresponds to the formula:
n = c / v.
The symbol c is the speed of electromagnetic waves in a vacuum. It is approximately 3 * 10 8 m / s. The value of v is the speed of light in the medium. Thus, the refractive index reflects the amount of light deceleration in the medium with respect to airless space.
Two important conclusions follow from the formula above:
- the value of n is always greater than 1 (for vacuum it is equal to unity);
- it is a dimensionless quantity.
For example, the refractive index of air is 1,00029, and for water it is 1.33.
The refractive index is not constant for a particular medium. It depends on the temperature. Moreover, for each frequency of the electromagnetic wave, it has its own meaning. So, the above numbers correspond to a temperature of 20 o C and the yellow part of the visible spectrum (wavelength - about 580-590 nm).
The dependence of n on the frequency of light is manifested in the decomposition of white light by a prism into a number of colors, as well as in the formation of a rainbow in the sky during heavy rain.
Refractive Index of Light in Air
Above, its value has already been given (1,00029). Since the refractive index of air differs only in the fourth decimal place from zero, it can be considered equal to unity to solve practical problems. A slight difference n for air from unity indicates that light is practically not slowed down by air molecules, which is associated with its relatively low density. So, the average value of the density of air is 1.225 kg / m 3 , that is, it is more than 800 times lighter than fresh water.
Air is an optically leaky medium. The process of slowing down the speed of light in a material is of a quantum nature and is associated with acts of absorption and emission of photons by atoms of a substance.
A change in the composition of the air (for example, an increase in the content of water vapor in it) and a change in temperature lead to significant changes in the refractive index. A striking example is the effect of a mirage in the desert, which occurs due to the difference in the refractive indices of air layers with different temperatures.
Glass - Air interface
Glass is a much denser medium than air. Its absolute refractive index ranges from 1.5 to 1.66, depending on the type of glass. If we take the average value of 1.55, then the refraction of the beam at the air-glass interface can be calculated by the formula:
sin (θ 1 ) / sin (θ 2 ) = n 2 / n 1 = n 21 = 1.55.
The value of n 21 is called the relative refractive index of air - glass. If the beam leaves the glass into the air, then the following formula should be used:
sin (θ 1 ) / sin (θ 2 ) = n 2 / n 1 = n 21 = 1 / 1.55 = 0.645.
If the angle of the refracted beam in the latter case is equal to 90 o , then the angle of incidence corresponding to it is called critical. For the glass-air boundary, it is equal to:
θ 1 = arcsin (0.645) = 40.17 o .
If the beam will fall on the border of glass - air with large angles than 40.17 o , then it will be reflected completely back into the glass. This phenomenon is called "full internal reflection."
The critical angle exists only when the beam moves from a dense medium (from glass to air, but not vice versa).