Refraction Definition

The redirection of a wave as it passes through one medium and then another is known as refraction in physics. The redirection could be caused by a change in the medium or a change in the wave's speed. Although refraction of light waves is the phenomenon that is most frequently observed, refraction of sound waves and water waves is also a possibility. How much a wave is refracted depends on the direction of the initial wave propagation in relation to the direction of the speed change and the change in wave speed.

The ratio of the sines of the angle of incidence and angle of refraction is equal to the phase velocities (v1/v2) or, alternately, the refractive indices (n2/n1) of the two media for a particular set of media, according to Snell's rule, which governs refraction of light. The human eye and optical prisms both employ refraction to direct light. The angle of refraction also fluctuates in accordance with the refractive index of the materials, which varies with light wavelength. Dispersion is the mechanism that separates white light into its component colours in prisms and rainbows.

Light

Refraction of light occurs regularly in everyday life. It makes objects under the water appear closer than they actually are. It serves as the basis for the creation of optical lenses, which are used to create objects like glasses, cameras, binoculars, microscopes, and the human eye. Just two examples of naturally occurring optical phenomena brought on by refraction are rainbows and mirages.

General justification

Refraction can be properly explained in the following two diverse ways, both of which arise from the fact that light is a wave:

1. Light slows down when passing through a substance other than a vacuum (such as air, glass or water). This is not a result of scattering or absorption. Instead, it is because light itself, which is an electromagnetic oscillation, induces the oscillation of other electrically charged particles, including electrons. The electromagnetic waves that the oscillating electrons produce, and release interact with the initial light. Wave packets in the resulting "combined" wave pass an observer more slowly. Effectively, the light has been slowed. When light returns to a vacuum and there are no electrons present, this slowing effect disappears, and light's speed returns to c.
2. One side of the wavefront slows down before the other when light enters a slower medium at an angle. The light's uneven slowing leads it to change its direction of travel. When entering the new medium with constant characteristics, light resumes its straight-line motion.

Explanation for why light in a medium is slowing down

As mentioned before, a medium other than vacuum has a slower speed of light. This slowing affects any media, including glass, water, and air, and is what causes phenomena like refraction. Without taking into account the effects of gravity, light's speed returns to the standard speed of light in a vacuum, or c, when it exits the medium and enters the vacuum. The widely accepted theories for this slowing-light scattering from atoms or light absorption and reemission-are both untrue. These types of explanations would result in a "blurring" of the resulting light because it would no longer be travelling in a single path. But nature does not exhibit this impact. The existence of light as an electromagnetic wave provides a valid explanation. The electrically charged electrons in a medium oscillate when light travels across it because light is an oscillating electrical/magnetic wave. (The material's protons oscillate as well, but due to their mass being around 2000 times greater, they move far less and have a much less influence.) Electromagnetic waves are generated by moving electrical charges. In a process known as constructive interference, which is comparable to water ripples on a pond, the electromagnetic waves that the oscillating electrons emit interact with the electromagnetic waves that make up the initial light. This type of interference between two waves might cause the resulting "combined" wave to include wave packets that move past an observer more slowly. The light has actually been slowed. The wave packet rate and resulting speed revert to normal when the light stops interfering with the material's electrons.

The reason why light bends when it enters and leaves a medium

As seen in the illustration, imagine a wave travelling from one substance to another where the speed is slower. One side of the wave will hit the second material first and slow down earlier if it approaches the contact between the materials at an angle. The entire wave will turn towards the side of the wave that is moving more slowly. This explains why, when a wave enters a slower material, it will bend away from the surface or in the direction of normal. A wave will accelerate on one side and pivot away from that side if it encounters a substance where the speed is higher.

Consider the shift in wavelength at the interface for another method to comprehend the same concept. When a wave goes from one material to another where the wave speed is different, the wavelength, or distance between wavefronts, or =v/f, varies. Yet, the wave's frequency does not change. The wavelength will likewise decrease if the speed is reduced, as shown in the right-hand picture. The wave fronts must maintain their integrity with an angle between them and the interface as well as a change in the distance between them. These elements allow for the deduction of a relationship between the angles of incidence and transmission and the wave velocity v1 and v2 in the two materials.

The 2- or 3-dimensional wave equation can be used to more directly deduce the phenomenon of refraction. The tangential component of the wave vector must then be the same on both sides of the interface in order to satisfy the boundary condition at the interface. The direction of the wave vector must change since the wave speed determines the wave vector's magnitude.

The phase velocity of the wave is the relevant wave speed in the previous discussion. It is crucial to utilise the phase velocity in any computations involving refraction even if this is frequently near to the group velocity, which is thought of as the more accurate speed of a wave. A wave that is travelling perpendicular to a boundary-that is, with its wavefronts parallel to the boundary-won't change direction even if its speed changes.

Law of refraction

When it comes to light, a material's refractive index (n) is more frequently employed than its wave phase speed (v).

Refraction in a water surface

Refraction occurs when light travels through a water surface because water has a refractive index of 1.33 and air has a refractive index of around 1. A straight object, like the pencil in the picture, that is only partially submerged in water, appears to bend at the water's surface. Light rays bend as they travel from the water to the air, which is what causes this. The eye follows the rays back as straight lines after they have reached it (lines of sight). The intersection of the lines of sight, shown by dashed lines, is higher than the origin of the rays. Due to this, the pencil and water appear taller and shallower than they actually are.

The apparent depth of a body of water refers to how deep it seems from above. This is an important consideration when spearfishing from the surface since it will cause the target fish to appear to be somewhere else and compel the fisher to aim lower in order to catch the fish. On the other hand, when seen from below the water, an object above it appears to be taller. The archer fish must make the opposite adjustment.

With modest angles of incidence, the refractive indices of air and water influence the ratio of apparent to true depth (measured from the normal, where sin and tan are almost equal). Yet, as the angle of incidence gets closer to 90 degrees, the perceived depth decreases, even though reflection is stronger, making it harder to observe at high angles of incidence. Yet, the picture likewise vanishes as this limit is approached. In contrast, when the angle of incidence (from below) increases, the apparent height reaches infinity, but even earlier once the angle of total internal reflection is reached.

Dispersion

Refraction is what causes rainbows and the splitting of white light into a rainbow spectrum as it travels through a glass prism. Glass has a higher refractive index than air. Dispersion is a phenomenon that happens when a beam of white light travels from the atmosphere into a medium with a variable index of refraction, causing the various coloured parts of the white light to be refracted at different angles and bend at the interface in different amounts, resulting in their separation. The various hues correspond to various frequencies.

Atmospheric refraction

The refractive index of air varies with air pressure and temperature because it is dependent on air density. Light rays that travel through the atmosphere for a long distance begin to refract towards the earth's surface because higher altitudes have lower pressure and a lower refractive index. It also slightly modifies the apparent positions of stars when they are close to the horizon, making the sun seem before it would otherwise rise above the horizon during a sunrise.

Variations in air temperature can also cause refraction of light. A heat haze results from the mixing of hot and cold air, which can happen over a fire, in vehicle exhaust, or when opening a window on a chilly day. As a result, items visible through the resulting mixed air appear to shimmer or drift aimlessly. When utilising high magnification telephoto lenses on a sunny day, this effect can also be seen. In these situations, the image quality is frequently constrained by this effect. Similar to this, atmospheric turbulence reduces the resolving power of terrestrial telescopes that don't use adaptive optics or other techniques to compensate for these atmospheric distortions. Air temperature changes near the surface can also result in other optical phenomena besides mirages and Fata Morgana. The air heated by a hot road most frequently deflects light coming at a shallow angle towards a spectator on a sunny day. Due to this, the road appears to be reflecting and appears to be covered in water.

Clinical significance

Refraction, also known as refractometry, is a clinical test done by the proper eye care expert to ascertain the eye's refractive error and the best corrective lenses to be given. It is most commonly employed in the fields of optometry, ophthalmology, and orthoptics. To identify which test lens offers the sharpest, clearest vision, a series of test lenses with varying optical powers or focal lengths are offered.

Mechanical waves

Water waves

Shallower water has slower-moving waves. This explains why waves near a beach often reach the ground at nearly a perpendicular angle and can be used to show refraction in ripple tanks. When waves transition from deep ocean to shallower water near the beach, they are refracted from their original direction of travel to a more normal angle to the shoreline.

Sound waves

The bending or curving of a sound beam as it travels through a gradient of sound speeds from one sound speed to another is known as refraction in underwater acoustics. The amount of ray bending depends on the difference in sound velocity or the difference in the temperature, salinity, and pressure of the water. The atmosphere of the Earth also shows comparable acoustic effects. Although sound refraction in the atmosphere has been observed for centuries, it wasn't until the early 1970s that this phenomena was widely studied due to the construction of metropolitan motorways and noise barriers to combat the meteorological effects of sound ray bending in the lower atmosphere.

Solved problems on refraction

1. Light travelling in air enters into an optical fibre of refractive index 1.44.

a) In which direction does the light bend?
b) If the angle of incidence on one end of the fibre is 22^o, then what is the angle of refraction?

Solution:

a) The light travels from a rarer medium(air) to a denser medium(optical fibre). Hence the refracted ray will bend towards the normal.
b) The angle of refraction can be calculated as follows:
Let air be medium 1 and optical fibre be medium 2. Therefore, n₁ = 1.00, n₂ = 1.44, and θ₁= 22^o.
Now, substituting the values in the equation as follows:
(1.00) sin 22^o = 1.44 sin θ₂.
sin θ₂ = (1.00/1.44) sin 22^o = 0.260
θ₂ = sin^-1 (0.260) = 15^o

2. The light travelling through the optical fibre reaches the end of the optical fibre and exits into the air. If the angle of incidence at the end of the tube is 30^o. Then what would the angle of refraction outside the fibre be?

Solution:

Let the fibre be medium 1 and air medium 2. Therefore, n₁ = 1.44, n₂ = 1.00, and θ,₁ = 30^o. Substituting the values in the equation, we get
(1.44) sin 30^o = 1.00 sin θ₂
sin θ₂ = (1.44/1.00) sin 30^o = 1.44 (0.500) = 0.720
θ₂ = sin^-1 (0.720) = 46^o
This time we notice that the angle of refraction is larger than the angle of incidence. This indicates that the light is bending away from the normal as it enters a rarer material.