Images in lenses, the operation of devices such as a microscope and telescope, the phenomenon of the rainbow and the deceptive perception of the depth of the reservoir are all examples of demonstrating the phenomenon of refraction of light. Laws describing this phenomenon are discussed in this article.
Refraction phenomenon
Before considering the laws of light refraction in physics, we will get acquainted with the essence of the phenomenon itself.
As you know, if the medium is homogeneous at all points in space, then the light will move in it along a straight path. The refraction of this trajectory occurs when a light beam crosses at an angle the interface between two transparent materials, for example, glass and water or air and glass. Having passed into another homogeneous medium, the light will also move in a straight line, but it will already be directed at a certain angle to its trajectory in the first medium. This is the phenomenon of refraction of a light beam.
The video below demonstrates the phenomenon of refraction by the example of glass.
An important point here is the angle of incidence on the media separation plane. From the value of this angle depends on whether the phenomenon of refraction is observed or not. If the beam falls perpendicular to the surface, then going into the second medium, it will continue to move along the same line. The second case, when refraction will not occur, are the angles of incidence of the beam coming from an optically denser medium to a less dense one, which are greater than some critical value. In this case, there will be a complete reflection of the light energy back to the first medium. The last effect is discussed below.
First law of refraction
It can also be called the law of three lines in one plane. Suppose there is a ray of light A that falls on the plane of separation of two transparent materials. At point O, the beam is refracted and begins to move along line B, which is not a continuation of A. If the perpendicular N is restored to point O to the interface, then the first law for the refraction phenomenon can be formulated as follows: incident beam A, normal N and refracted beam B lie in one plane, which is perpendicular to the plane of separation of media.
This simple law is not obvious. Its formulation is the result of a generalization of experimental data. Mathematically, it can be deduced by using the so-called Fermat principle or the principle of least time.
Second law of refraction
From school physics teachers, schoolchildren often receive the following task: "Formulate the laws of light refraction." We have considered one of them, now we will pass to the second.
We denote the angle between beam A and perpendicular N as θ 1 , the angle between beam B and N is called θ 2 . We also take into account that the speed of beam A in medium 1 is equal to v 1 , and the speed of beam B in medium 2 is equal to v 2 . Now we can give a mathematical formulation of the 2nd law for the phenomenon under consideration:
sin (θ 1 ) / v 1 = sin (θ 2 ) / v 2 .
This formula was obtained by the Dutch Snell at the beginning of the 17th century and now bears his last name.
An important conclusion follows from the expression: the greater the speed of light propagation in the medium, the farther away from the normal the beam will be (the sine of the angle is larger).
The concept of the refractive index of the medium
The above Snell formula is currently written in a slightly different form, which is more convenient to use when solving practical problems. Indeed, the speed v of light in a substance, although less than that in a vacuum, is nevertheless a large quantity with which it is difficult to work. Therefore, a relative quantity was introduced into physics, the equality for which is presented below:
n = c / v.
Here c is the speed of the beam in vacuum. The value of n shows how many times the value of c is greater than the value of v in the material. It is called the refractive index of this material.
Given the entered value, the formula for the law of refraction of light will be rewritten in the following form:
sin (θ 1 ) * n 1 = sin (θ 2 ) * n 2 .
A material with a large n value is called optically dense. Passing through it, the light slows down its speed n times compared with the same value for airless space.
This formula shows that the beam will lie closer to the normal in the medium that is more optically dense.
For example, we note that the refractive index for air is almost equal to unity (1,00029). For water, its value is 1.33.
Total reflection in an optically dense medium
We will carry out the following experiment: we will let out a ray of light from the water column towards its surface. Since water is optically denser than air (1.33> 1,00029), the angle of incidence θ 1 will be less than the angle of refraction θ 2 . Now, we will gradually increase θ 1 , and θ 2 will increase accordingly, while the inequality θ 1 <θ 2 always remains true.
The moment will come when θ 1 <90 o , and θ 2 = 90 o . This angle θ 1 is called critical for a pair of water-air media. Any angles of incidence that are larger than this will lead to the fact that no part of the beam passes through the water-air interface into a less dense medium. The entire beam at the boundary will experience full reflection.
The calculation of the critical angle of incidence θ c is performed by the formula:
θ c = arcsin (n 2 / n 1 ).
For media, water and air, it is equal to 48.77 o .
Note that this phenomenon is not reversible, that is, when the light moves from air to water, a critical angle does not exist.
The described phenomenon is used in the operation of optical fibers, and together with the dispersion of light is the cause of the appearance of primary and secondary rainbows during rain.