Refraction

In physics, refraction denotes the redirection of a wave as it transitions from one medium to another. This deviation can be attributed to a change in the wave's speed or an alteration in the medium itself. While the refraction of light is the most frequently observed phenomenon, other wave types, such as sound and water waves, also undergo refraction. The magnitude of a wave's refraction is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of the speed alteration.

In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.

Optical prisms, lenses, and the human eye all employ refraction for light manipulation. The refractive index of materials is dependent on the wavelength of light, and consequently, the angle of refraction exhibits a corresponding variation. This phenomenon, termed dispersion, enables prisms and atmospheric water droplets in rainbows to separate white light into its constituent spectral colors.

Law

For light, refraction adheres to Snell's law, which postulates that, for any specific pair of media, the ratio of the sines of the angle of incidence θ<!-- θ --> §1213§ {\displaystyle {\theta _{1}}} and the angle of refraction ${\displaystyle {\theta _{2}}}$ is equivalent to the ratio of the phase velocities v §6263§ v §7071§ {\textstyle {\frac {v_{1}}{v_{2}}}} within the two media, or, alternatively, to the inverse ratio of their respective refractive indices n §9697§ n §104105§ {\textstyle {\frac {n_{2}}{n_{1}}}} :

sin ⁡<!-- ⁡ --> θ<!-- θ --> §1920§ sin ⁡ θ §3536§ = v §5051§ v §5859§ = n §7273§ n §8081§ {\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}={\frac {n_{2}}{n_{1}}}}

Conceptual Overview

General explanation

Refraction encompasses two interconnected phenomena, both stemming from the wave-like properties of light: a diminution in velocity within an optical medium and an angular deviation as a wavefront traverses the interface between distinct media at an oblique angle.

1. When light propagates through a medium other than a vacuum (e.g., air, glass, or water), its speed decreases. This deceleration is not attributable to scattering or absorption. Instead, light, functioning as an electromagnetic oscillation, induces oscillations in other electrically charged particles, such as electrons. These oscillating electrons subsequently emit their own electromagnetic waves, which then interact with the initial light. The resultant composite wave exhibits a reduced propagation speed. Upon returning to a vacuum, where no electrons are present, this slowing effect ceases, and the light's speed reverts to c.
2. If light enters a denser medium at an oblique angle, one portion of the wavefront experiences deceleration prior to the other. This differential slowing of the light compels a change in its direction of propagation. Once the light is fully immersed within the new medium, assuming uniform properties, it resumes travel in a rectilinear path.

Light Deceleration

As previously explained, light propagates at a reduced speed within any medium distinct from a vacuum. This deceleration is observed across various media, including air, water, and glass, and underlies phenomena like refraction. Upon exiting such a medium, the light's speed reverts to its vacuum velocity, c.

A precise explanation for this phenomenon is predicated on light's inherent nature as an electromagnetic wave. As an oscillating electrical and magnetic wave, light traversing a medium induces oscillations in the electrically charged electrons within that material. (While the material's protons also oscillate, their significantly greater mass—approximately 2000 times that of electrons—renders their movement and consequent effect negligible). A moving electrical charge inherently emits its own electromagnetic waves. The electromagnetic waves generated by these oscillating electrons then interact with the original electromagnetic waves constituting the incident light. This interaction, analogous to the superposition of water waves on a pond, is termed constructive interference. When two waves interfere in this manner, the resultant "combined" wave can exhibit wave packets that propagate past an observer at a diminished rate, effectively slowing the light. Upon the light's exit from the material, this electron interaction ceases, causing the wave packet rate, and thus its speed, to revert to its original value.

Light Refraction

Envision a wave transitioning from one medium to another where its propagation speed is reduced, as depicted in the accompanying figure. Should the wave encounter the interface between these materials at an angle, one segment of the wavefront will enter the second material first, consequently decelerating sooner. This differential slowing causes the entire wavefront to pivot towards the slower side. This mechanism explains why a wave bends away from the surface or towards the normal when entering a slower medium. Conversely, if a wave encounters a material where its speed increases, one side of the wave will accelerate, causing the wave to pivot away from that side.

Alternatively, this phenomenon can be comprehended by examining the alteration in wavelength at the interface. When a wave transitions from one material to another where its speed v differs, the wave's frequency f remains constant, but the inter-wavefront distance, or wavelength λ = v/f, undergoes a change. If the speed diminishes, as illustrated in the figure to the right, the wavelength will similarly decrease. Given an angle between the wavefronts and the interface, coupled with a change in the distance between wavefronts, the angle must adjust across the interface to maintain wavefront coherence. Based on these principles, the relationship between the angle of incidence θ§1516§, the angle of transmission θ§2122§, and the wave speeds v§2728§ and v§3334§ within the two respective materials can be derived. This fundamental relationship is known as the law of refraction, or Snell's Law, and is expressed as

sin ⁡<!-- ⁡ --> θ<!-- θ --> §1920§ sin ⁡ θ §3536§ = v §5051§ v §5859§ . {\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}\,.}

Fundamentally, the phenomenon of refraction can be derived from the two- or three-dimensional wave equation. The boundary condition at the interface mandates that the tangential component of the wave vector remains identical across both sides of the interface. Consequently, as the magnitude of the wave vector is contingent upon the wave speed, a directional alteration of the wave vector becomes necessary.

The pertinent wave speed in the preceding analysis is the wave's phase velocity. While this typically approximates the group velocity, often considered the true wave speed, it is crucial to employ the phase velocity in all refraction-related calculations when these two velocities diverge.

A wave propagating perpendicularly to a boundary, with its wavefronts parallel to the interface, will not undergo a change in direction, even if the wave's speed varies.

Dispersion of Light

Refraction is also responsible for the formation of rainbows and for the separation of white light into its constituent rainbow spectrum when it traverses a glass prism. Both glass and water possess higher refractive indices than air. When a beam of white light transitions from air into a material whose refractive index varies with frequency (and wavelength), a phenomenon known as dispersion occurs. During dispersion, different colored components of the white light are refracted at distinct angles, meaning they bend by varying amounts at the interface, leading to their separation. These distinct colors correspond to different frequencies and wavelengths.

Refraction in Water

Refraction manifests when light traverses a water surface, given that water possesses a refractive index of 1.33, while air has an approximate refractive index of 1. When observing a straight object, such as a pencil depicted in an accompanying figure, positioned obliquely and partially submerged, the object appears to bend at the water's interface. This optical illusion results from the deflection of light rays as they transition from water to air. Upon reaching the observer's eye, these rays are perceived as originating from straight lines, or lines of sight. These perceived lines of sight (often represented as dashed lines) converge at an elevated position compared to the actual origin of the rays. Consequently, the pencil appears elevated, and the water body seems shallower than its true depth.

The perceived depth of water when viewed from above is termed the apparent depth. This concept is critically important for spearfishing from the surface, as it causes the target fish to appear in a different location, necessitating that the fisher aims lower to successfully catch the fish. Conversely, an object situated above the water exhibits a greater apparent height when observed from beneath the water. An archer fish must apply the inverse correction.

For small angles of incidence (measured from the normal, where sin θ is approximately equivalent to tan θ), the ratio of apparent depth to real depth corresponds to the ratio of the refractive indices of air to water. However, as the angle of incidence approaches 90°, the apparent depth converges towards zero, although reflection simultaneously increases, thereby limiting observation at high angles of incidence. Conversely, the apparent height approaches infinity as the angle of incidence (from below) increases, but even earlier, as the angle of total internal reflection is approached, the image also diminishes from view.

Atmospheric Refraction

The refractive index of air is contingent upon its density, which in turn fluctuates with temperature and pressure. At elevated altitudes, reduced atmospheric pressure leads to a diminished refractive index. This phenomenon causes light rays traversing extensive atmospheric distances to refract towards the Earth's surface, resulting in a slight displacement of the apparent positions of stars near the horizon and rendering the sun visible prior to its geometric ascent during sunrise.

Fluctuations in air temperature similarly induce light refraction, manifesting as a heat haze when disparate air masses intermingle, such as above a fire, within engine exhaust, or upon opening a window on a cold day. This optical distortion causes objects observed through the turbulent air to appear to shimmer or undergo random displacement as the air currents shift. Furthermore, typical diurnal air temperature variations on sunny days can produce this effect, often compromising image quality when utilizing high-magnification telephoto lenses. Analogously, atmospheric turbulence introduces rapid and variable distortions in astronomical telescope images, thereby constraining the resolution of terrestrial telescopes that do not employ adaptive optics or comparable atmospheric distortion mitigation techniques.

Near-surface air temperature gradients can generate additional optical phenomena, including mirages and Fata Morgana. A prevalent example involves air heated by an asphalt surface on a sunny day, which refracts light incident at a shallow angle towards an observer. This refraction creates the illusion of a reflective surface, often perceived as water covering the road.

In Eye Care

Within the medical fields of optometry, ophthalmology, and orthoptics, refraction (alternatively termed refractometry) constitutes a clinical assessment. During this procedure, a qualified eye care professional employs a phoropter to ascertain the eye's refractive error and to prescribe the most suitable corrective lenses. The process involves presenting a sequence of test lenses with varying optical powers or focal lengths to identify the combination that yields the sharpest and clearest visual acuity. Additionally, refractive surgery represents a medical intervention designed to address prevalent vision disorders.

Mechanical Waves

Water

Water waves exhibit a reduction in velocity when propagating through shallower depths. This principle facilitates the demonstration of refraction in ripple tanks and elucidates why shoreline waves typically approach the coast at an angle approximating perpendicularity. As waves transition from deeper offshore waters to the shallower nearshore region, their trajectory is refracted from the original direction of propagation towards an angle more orthogonal to the shoreline.

Sound

In underwater acoustics, refraction refers to the deflection or curvature of a sound ray as it traverses a sound speed gradient, moving from an area of one sound velocity to another. The extent of this ray bending is directly proportional to the disparity in sound speeds, which is influenced by variations in water temperature, salinity, and pressure. Analogous acoustic phenomena are also observed within the Earth's atmosphere. The atmospheric refraction of sound has been recognized for centuries; however, comprehensive analysis of this effect gained prominence in the early 1970s, particularly in the context of designing urban highways and noise barriers to mitigate the meteorological influences on sound ray propagation in the lower atmosphere.

Gallery

• Birefringence (double refraction)
• Huygens–Fresnel principle
• Negative refraction
• Schlieren photography
• Super refraction

References

• Reflections and Refractions in Ray Tracing, a simple but thorough discussion of the mathematics behind refraction and reflection.
• "Refraction" . In Encyclopædia Britannica, Vol. 23 (11th ed.), 1911, pp. 25–29.
• "Refraction" . Encyclopædia Britannica. Vol. 23 (11th ed.). 1911. pp. 25–29.Source: TORIma Academy Archive