Question

Why does refraction happen? That is, what is the physical reason a wave moves in a new medium with a different velocity than it did in the original medium?

Short answer

Answer: Refraction occurs when a wave moves from one medium to another due to the change in the wave's velocity as it encounters differing properties (such as elasticity and density) in the new medium. This change in velocity alters the wave's direction, following Snell's Law. The interaction between wavefronts and Huygens' Principle also helps explain this change in direction, as wavelets in the new medium have a different curvature due to their changed velocity.

Step-by-step solution

Understand the wave's velocity in different media

When a wave travels through a medium, its velocity depends on the properties of that medium such as elasticity and density. Different media have different elastic and density properties, which can affect how fast or slow a wave can travel through them. For example, light waves travel faster in air than in water or glass because air has a lower refractive index. The refractive index is a measure of how much the speed of light is reduced in a particular medium relative to its speed in a vacuum.

Snell's Law and the change in direction

Refraction can be described by Snell's Law: n1 * sin(theta1) = n2 * sin(theta2) where n1 and n2 are the refractive indices of the two media, and theta1 and theta2 are the angles of incidence and refraction, respectively. When a wave moves from one medium to another, the change of medium causes a difference in the wave's velocity which impacts the wavefronts. As a result, the direction of the wave changes to adjust to the new speed, following Snell's Law.

Wavefronts and Huygens' Principle

When a wave travels from one medium to another, the individual wavefronts encounter the boundary between the two media at different times. According to Huygens' Principle, each point on the wavefront acts as a source of new wavelets. The wavelets from different points in the new medium travel at the new velocity and recombine to form a new wavefront. As the wavelets in the new medium have a different velocity, their curvature is different from the wavefronts in the initial medium. This change in curvature leads to a change in direction of the overall wave, which is the effect of refraction.

Summary

In conclusion, refraction happens due to the change in velocity of a wave when it moves from one medium to another with different properties (elasticity and density), altering the wave's direction. This change in direction obeys Snell's Law and can be further explained by the interaction of wavefronts and Huygens' Principle.

Key concepts

Snell's Law

Snell's Law is a fundamental concept in wave optics that explains how a wave, such as light or sound, bends, or refracts, when it travels from one medium to another with a different refractive index. This law is mathematically expressed as:
\( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \)
where \( n_1 \) and \( n_2 \) represent the refractive indices of the original and new medium, respectively, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction. The refractive index is a dimensionless number that describes how light propagates through that medium compared to the speed of light in a vacuum.
Snell's Law is critical for understanding phenomena like the bending of a straw in water or the splitting of light into a rainbow by a prism. The ability to calculate the change of angle can also help in designing lenses for glasses and cameras to ensure proper light direction and focus.

Huygens' Principle

Huygens' Principle lays the groundwork for understanding wave phenomena including refraction, reflection, diffraction, and interference. It proposes that every point on a wavefront is a source of spherical secondary wavelets, which spread out in the forward direction at the speed characteristic to that medium. After a certain amount of time, the new position of the wavefront is the tangential surface to these secondary wavelets.
Applying Huygens' Principle to Refraction
When dealing with refraction, Huygens' Principle helps to visualize how a planar wavefront changes as it crosses the boundary between two media with different wave velocities. The secondary wavelets in the slower medium will lag behind those in the faster medium, causing the wavefront to bend at a different angle, as predicted by Snell's Law. This principle is fundamental not just in theoretical studies but also in practical applications like the creation of holograms and understanding seismic wave propagation.

Refractive Index

The refractive index, often denoted as \( n \), is a measure that indicates how much the speed of light is changed when it enters a material. A higher refractive index indicates that light travels slower in that medium compared to a medium with a lower refractive index. The refractive index of a vacuum is 1, and air is approximately 1.003, which are used as reference points.
Refractive index and optical materials
Materials with varying refractive indices are selected for lenses and other optical devices based on desired light-bending properties. For example, a material with a high refractive index will bend light more than one with a lower refractive index, which is a principle exploited in corrective eyewear and photography. Understanding this concept is essential in designing a multitude of optical devices and in studying the behavior of light in different environments.

Wave Velocity

Wave velocity is the speed at which a wave propagates through a medium. This speed can be affected by the medium's physical properties, such as its elasticity, density, and temperature. For example, sound waves travel faster in solids than in liquids, and even faster in gases, because of the differences in these properties.
Factors affecting wave velocity
While elasticity tends to increase wave speed, higher density typically reduces it. In the context of light, the velocity depends on the optical density of the medium and is inversely proportional to the refractive index. Light, therefore, travels at its maximum speed in a vacuum, with the velocity in any other medium being a fraction of this.
Understanding wave velocity is crucial not only in basic physics but also in diverse fields like meteorology, oceanography, and telecommunications, where the transmission and interpretation of waves are fundamental to operations.