One of the important laws of light wave propagation in transparent substances is the law of refraction, formulated at the beginning of the 17th century by the Dutchman Snell. The parameters that appear in the mathematical formulation of the phenomenon of refraction are the indices and angles of refraction. This article discusses how light rays behave when passing through the surface of different media.
What is the phenomenon of refraction?
The main property of any electromagnetic wave is its rectilinear motion in a homogeneous (homogeneous) space. When any inhomogeneity occurs, the wave experiences more or less deviation from the rectilinear trajectory. This inhomogeneity may be the presence of a strong gravitational or electromagnetic field in a certain region of space. In this article, these cases will not be considered, but attention will be paid to the inhomogeneities associated with the substance.
The effect of refraction of a ray of light in its classical formulationmeans a sharp change from one rectilinear direction of motion of this beam to another when passing through the surface that delimits two different transparent media.
The following examples satisfy the definition given above:
- beam transition from air to water;
- from glass to water;
- from water to diamond etc.
Why does this phenomenon occur?
The only reason for the described effect is the difference in the velocities of electromagnetic waves in two different media. If there is no such difference, or it is insignificant, then when passing through the interface, the beam will retain its original direction of propagation.
Different transparent media have different physical density, chemical composition, temperature. All these factors affect the speed of light. For example, the phenomenon of a mirage is a direct consequence of the refraction of light in layers of air heated to different temperatures near the earth's surface.
Main laws of refraction
There are two of these laws, and anyone can check them if they are armed with a protractor, a laser pointer and a thick piece of glass.
Before formulating them, it is worth introducing some notation. The refractive index is written as ni, where i - identifies the corresponding medium. The angle of incidence is denoted by the symbol θ1 (theta one), the angle of refraction is θ2 (theta two). Both angles countrelative not to the separation plane, but to the normal to it.
Law 1. The normal and two rays (θ1 and θ2) lie in the same plane. This law is completely similar to the 1st law for reflection.
Law No. 2. For the phenomenon of refraction, the equality is always true:
1 sin (θ1)=n2 sin (θ 2).
In the above form, this ratio is the easiest to remember. In other forms, it looks less convenient. Below are two more options for writing Law 2:
sin (θ1) / sin (θ2)=n2 / n1;
sin (θ1) / sin (θ2)=v1 / v2.
Where vi is the speed of the wave in the i-th medium. The second formula is easily obtained from the first by direct substitution of the expression for ni:
i=c / vi.
Both of these laws are the result of numerous experiments and generalizations. However, they can be obtained mathematically using the so-called principle of least time or Fermat's principle. In turn, Fermat's principle is derived from the Huygens-Fresnel principle of secondary wave sources.
Features of Law 2
1 sin (θ1)=n2 sin (θ 2).
It can be seen that the greater the exponent n1 (a dense optical medium in which the speed of light decreases greatly), the closer will be θ1 to the normal (the function sin (θ) monotonically increases bysegment [0o, 90o]).
The refractive indices and velocities of electromagnetic waves in media are tabular values measured experimentally. For example, for air, n is 1.00029, for water - 1.33, for quartz - 1.46, and for glass - about 1.52. Strongly light slows down its movement in a diamond (almost 2.5 times), its refractive index is 2.42.
The given figures say that any transition of the beam from the marked media into the air will be accompanied by an increase in the angle (θ2>θ1). When changing the direction of the beam, the opposite conclusion is true.
The refractive index depends on the frequency of the wave. The above figures for different media correspond to a wavelength of 589 nm in vacuum (yellow). For blue light, these figures will be slightly higher, and for red - less.
It is worth noting that the angle of incidence is equal to the angle of refraction of the beam only in one single case, when the indicators n1 and n2 are the same.
The following are two different cases of application of this law on the example of media: glass, air and water.
The beam passes from air to glass or water
There are two cases worth considering for each environment. You can take for example the angles of incidence 15o and 55o on the border of glass and water with air. The angle of refraction in water or glass can be calculated using the formula:
θ2=arcsin (n1 / n2 sin (θ1)).
The first medium in this case is air, i.e. n1=1, 00029.
Substituting the known angles of incidence into the expression above, we get:
for water:
(n2=1, 33): θ2=11, 22o (θ1 =15o) and θ2=38, 03 o (θ1 =55o);
for glass:
(n2=1, 52): θ2=9, 81o (θ1 =15o) and θ2=32, 62 o (θ1 =55o).
The data obtained allow us to draw two important conclusions:
- Since the angle of refraction from air to glass is smaller than for water, the glass changes the direction of the rays a little more.
- The greater the angle of incidence, the more the beam deviates from the original direction.
Light moves from water or glass into air
It is interesting to calculate what the angle of refraction is for such a reverse case. The calculation formula remains the same as in the previous paragraph, only now the indicator n2=1, 00029, that is, corresponds to air. Get
when the beam moves out of the water:
(n1=1, 33): θ2=20, 13o (θ1=15o) and θ2=does not exist (θ 1=55o);
when the glass beam moves:
(n1=1, 52): θ2=23,16o(θ1 =15o) and θ2=does not exist (θ1=55o).
For the angle θ1 =55o, the corresponding θ2 cannot be determined. This is due to the fact that it turned out to be more than 90o. This situation is called total reflection inside an optically dense medium.
This effect is characterized by critical angles of incidence. You can calculate them by equating in law No. 2 sin (θ2) to one:
θ1c=arcsin (n2/ n1).
Substituting the indicators for glass and water into this expression, we get:
for water:
(n1=1, 33): θ1c=48, 77o;
for glass:
(n1=1, 52): θ1c=41, 15o.
Any angle of incidence that is greater than the values obtained for the corresponding transparent media will result in the effect of total reflection from the interface, i.e. no refracted beam will exist.
