Optics And Refraction Pdf Free Download

When a wave travels across an interface and into a medium with a higher index of refraction, the wave bends towards the normal. If a wave travels across an interface and into a lower index of refraction, the wave bends away from the normal. If a wave travels across an interface and into a medium with the same index of refraction, the direction of the wave's propagation does not change. The two most common indices of refraction used when first exploring the topic of refraction are air ( n = 1.00029 {\displaystyle n=1.00029} ) and water ( n = 1.33 {\displaystyle n=1.33} ). To simplify calculations, the index of refraction of air is typically approximated to be n = 1.00 {\displaystyle n=1.00} (which is actually the index of refraction of a vacuum).

As the angle of incidence increases, the angle of refraction also increases. There comes a point in which the angle of refraction is 90 and means that the wave refracts parallel to the interface. This angle is called the critical angle and for angles greater than or equal to the critical angle, refraction does not take place and all of the light is reflected; this phenomenon is called total internal reflection and will be covered in the next section.

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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.[1] 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 and lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the wavelength of light,[3] and thus the angle of the refraction also varies correspondingly. This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors.[4]

As described above, the speed of light is slower in a medium other than vacuum. This slowing applies to any medium such as air, water, or glass, and is responsible for phenomena such as refraction. When light leaves the medium and returns to a vacuum, and ignoring any effects of gravity, its speed returns to the usual speed of light in vacuum, c.

Another way of understanding the same thing is to consider the change in wavelength at the interface. When the wave goes from one material to another where the wave has a different speed v, the frequency f of the wave will stay the same, but the distance between wavefronts or wavelength tag_hash_130=v/f will change. If the speed is decreased, such as in the figure to the right, the wavelength will also decrease. With an angle between the wave fronts and the interface and change in distance between the wave fronts the angle must change over the interface to keep the wave fronts intact. From these considerations the relationship between the angle of incidence 1, angle of transmission 2 and the wave speeds v1 and v2 in the two materials can be derived. This is the law of refraction or Snell's law and can be written as[6]

The phenomenon of refraction can in a more fundamental way be derived from the 2 or 3-dimensional wave equation. The boundary condition at the interface will then require the tangential component of the wave vector to be identical on the two sides of the interface.[7] Since the magnitude of the wave vector depend on the wave speed this requires a change in direction of the wave vector.

The relevant wave speed in the discussion above is the phase velocity of the wave. This is typically close to the group velocity which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction.

Refraction is also responsible for rainbows and for the splitting of white light into a rainbow-spectrum as it passes through a glass prism. Glass has a higher refractive index than air. When a beam of white light passes from air into a material having an index of refraction that varies with frequency, a phenomenon known as dispersion occurs, in which different coloured components of the white light are refracted at different angles, i.e., they bend by different amounts at the interface, so that they become separated. The different colors correspond to different frequencies.

Temperature variations in the air can also cause refraction of light. This can be seen as a heat haze when hot and cold air is mixed e.g. over a fire, in engine exhaust, or when opening a window on a cold day. This makes objects viewed through the mixed air appear to shimmer or move around randomly as the hot and cold air moves. This effect is also visible from normal variations in air temperature during a sunny day when using high magnification telephoto lenses and is often limiting the image quality in these cases.[9] In a similar way, atmospheric turbulence gives rapidly varying distortions in the images of astronomical telescopes limiting the resolution of terrestrial telescopes not using adaptive optics or other techniques for overcoming these atmospheric distortions.

In medicine, particularly optometry, ophthalmology and orthoptics, refraction (also known as refractometry) is a clinical test in which a phoropter may be used by the appropriate eye care professional to determine the eye's refractive error and the best corrective lenses to be prescribed. A series of test lenses in graded optical powers or focal lengths are presented to determine which provides the sharpest, clearest vision.[10]Refractive surgery is a medical procedure to treat common vision disorders.

Water waves travel slower in shallower water. This can be used to demonstrate refraction in ripple tanks and also explains why waves on a shoreline tend to strike the shore close to a perpendicular angle. As the waves travel from deep water into shallower water near the shore, they are refracted from their original direction of travel to an angle more normal to the shoreline.[11]

In underwater acoustics, refraction is the bending or curving of a sound ray that results when the ray passes through a sound speed gradient from a region of one sound speed to a region of a different speed. The amount of ray bending is dependent on the amount of difference between sound speeds, that is, the variation in temperature, salinity, and pressure of the water.[12]Similar acoustics effects are also found in the Earth's atmosphere. The phenomenon of refraction of sound in the atmosphere has been known for centuries;[13] however, beginning in the early 1970s, widespread analysis of this effect came into vogue through the designing of urban highways and noise barriers to address the meteorological effects of bending of sound rays in the lower atmosphere.[14]

Refractive index is defined as the relative speed at which light moves through a material with respect to its speed in a vacuum. By convention, the refractive index of a vacuum is defined as having a value of 1.0. The index of refraction, n, of other transparent materials is defined through the equation:

where n represents the refractive indices of material 1 and material 2 and q symbolizes the angles of light traveling through these materials with respect to the normal. There are several important points that can be drawn from this equation. When n(1) is greater than n(2), the angle of refraction is always smaller than the angle of incidence. Alternatively, when n(2) is greater than n(1) the angle of refraction is always greater than the angle of incidence. When the two refractive indices are equal (n(1) = n(2)), then the light is passed through without refraction.

The concept of refractive index is illustrated in Figure 1 below, focusing on the case of light passing from air through both glass and water. Notice that while both beams enter the denser material through the same angle of incidence with respect to the normal (60 degrees), the refraction for glass is almost 6 degrees greater than that for water due to the higher refractive index of glass.

Scientists have found that the index of refraction varies with the frequency of radiation (or wavelength) of light. This phenomenon occurs in conjunction with all transparent media and has been termed dispersion. Therefore, when measuring the refractive index of a transparent substance, the particular wavelength used in the measurement must be identified. Below, Table 2 details the dispersion of three independent wavelengths in various media.

Due to the refraction of light, a common optical illusion occurs when objects are visualized in water. A simple drinking straw in a glass filled with water, as illustrated in Figure 3, is a prime example of this occurrence. In this example, waves of light must first pass through the water, then through the glass/water boundary, and finally through the air. The light waves reflected from the ends of the straw are refracted to a greater degree than those coming from the center of the straw, making the straw appear magnified and slightly distorted.

The critical angle of reflection is another key concept in the study of light refraction and is illustrated below in Figure 4. When light passes through a medium of high refractive index into a medium of lower refractive index, the incident angle of the light waves becomes an important factor. If the incident angle increases past a specific value (dependent upon the refractive index of the two media), it will reach a point where the angle is so large that no light is refracted into the medium of lower refractive index.

In Figure 4, individual light rays are represented by either red or yellow colored arrows moving from a medium of high refractive index (n(2)) to one of lower refractive index (n(1)). The angle of incidence of each individual light ray is denoted by i and the angle of refraction by r. The four yellow light rays all have an angle of incidence (i) low enough to pass through the interface between the two media. However, the two red light rays have incident angles that exceed the critical angle (approximately 41 degrees) and are reflected either into the boundary between the media or back into the high refractive index medium. This phenomenon takes place when the angle of refraction (angle r in Figure 4) becomes equal to 90 degrees and Snell's law reduces to: 2351a5e196