This change can only occur if the wave falls obliquely on the area of separation of the two media, and if they have different refractive indices. The law then explains to us that the product of the refractive index by the sine of the angle of incidence is constant for any ray of light striking the surface of two media.
Willebrord Snell van Royen was an astronomer and mathematician of Dutch origin who was born in in Leiden, and who died in He began to study law , but his main interest was mathematics. Apparently, it was first mentioned by Ibn Sahl in the 10th century. In the term was again taken into consideration by Thomas Harriot , but he did not publish it. Many scientists had analyzed that light rays changed direction when they came into contact with a denser surface, but Snell discovered the exact law in Although this law was created in order to explain the refraction phenomena of light, it can also be applied to all types of waves that are passing through a surface of separation between two media in which the velocity of propagation of the wave varies.
Refraction, in physics , refers to the change in the direction of a wave passing from one medium to another caused by its change in velocity. Light is refracted each time it travels at an angle towards a substance with a different refractive index, which is what we know as optical density.
This change in direction is caused by a change in velocity. It occurs when the speed of the light varies while traveling through the two different mediums. Consider the two different mediums air and water. When the light travels from the first medium air to the second water medium, the light ray is refracted towards or away from the interface normal line. The angle of refraction depends on the relative refractive index of the two mediums.
The angle of refraction is high when the light ray propagates away from the normal. When the refractive index of the second material is higher than the refractive index of the first material, then the refracted ray propagates towards the normal and the angle of refraction is small. This gives the total internal reflection. That means, when light ray travels from lower medium to higher medium, it bends towards the normal with respect to the interface.
The refractive index of the material depends on the wavelength. If the wavelength is high, the refractive index would be low. If the index of refraction for the second material is greater than the first material, then the light will be refracted to a smaller angle.
Snell's Law arises from the wave nature of light. Light can be described in one of several ways: a ray, a particle photon , and as a wave. The interaction of light with a material can be best described for light when light is thought of as a wave.
The key to understanding the behavior of light at an interface is that Energy must be conserved: the energy of light going in the first material must be the same as the energy of the light in the second material. The energy of light can be described in the following way:. Because energy must be conserved at the boundary, the frequency of the light must remain the same for all materials.
This is because the number of waves arriving at the interface per unit time must be the same as the number of waves leaving the interface per unit time; the boundary interface cannot create or destroy waves. This concept is shown in Figure 2.
Figure 2: The number of wavefronts arriving at the interface must be the same at the number leaving the interface. However, the speed that a wave propagates at is dependent on the medium the light is traveling in. This velocity change is due to the interaction between light and the resonance of the electrons in the material which are either tightly or loosely held to the nuclei in the material. It is this change in velocity that causes the refraction of light in a new medium. An important extension of Snell's law is the concept of Total Internal Reflection and the critical angle.
For any combination of mediums, there is an angle for which the refracted light will be perpendicular to the normal Figure 3.
The critical angle is given by the equati on:. If the incident angle is greater than the critical angle, the light will be completely reflected back into the original medium. This is shown in the last image of Figure 3. Total Internal Reflection can also occur if there is a significant difference in the refractive index between the two materials. It is this type of total internal reflection that gives rise to fiber optics.
A very important application of Snell's Law is Fiber Optics. Fiber Optics are used for many applications, from telecommunications to data transmission in high speed servers. Because the fibers are not laid out in straight lines, the light must be guided down the length of the fiber. This is achieved with one of three types of fiber: step-index fiber, graded-index fiber multimode , or single-mode fiber. These fiber types are shown in Figure 4. Figure 4: Schematics and comparison of Fiber Optic Cable types.
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