From historical times, analogies between mechanics and optics have enriched both fields and have led to better understanding of both the fields leading to development of technology and multiple applications. The field is still at its infancy and more is yet to come, as mechanics continues to provide momentum to new optical discoveries and optics sheds light on novel explanations of the mechanics of nature.

Today, the analogies between mechanics and optics, are leading to the development of extreme technologies such as cloaking devices for invisibility (remember Harry Potter and the cloak of invisibility) and artificial materials (e.g. metamaterials) with properties not found in nature, while continuing to provide fundamental insights in the physical sciences in domains as far reaching as gravitational astrophysics and nonlinear fluid dynamics.

The development of this led to the very interesting and important field of calculus of variations and forms the basis of the field of mechanics (through what is known as the Hamilton’s principle of least action (William Roland Hamilton (1805-1865)) and also in optics (through Fermat’s principle of least time). It was Leonhard Euler (1707-1783), the Swiss genius (and a student of Johann Bernoulli) who in collaboration with Joseph Louis Lagrange (1736-1813), derived the now famous Euler-Lagrange equations when he was just 19 years old! These equations have an exceeding number of applications in science, engineering, economics, and medicine. (Fun fact: Euler is the only mathematician to have two numbers named after him: e (Euler number) and g (Euler constant) and who popularized the use of the Greek letter π to denote the ratio of a circle’s circumference to its diameter.)

Lens mirror and prism definitionphysics

Dispersive prisms are used to break up light into its constituent spectral colors because the refractive index depends on wavelength; the white light entering the prism is a mixture of different wavelengths, each of which gets bent slightly differently. Blue light is slowed more than red light and will therefore be bent more than red light.

Prisms made of isotropic materials like glass will also alter polarization of light, as partial reflection under oblique angles does not maintain the amplitude ratio (nor phase) of the s- and p-polarized components of the light, leading to general elliptical polarization. This is generally an unwanted effect of dispersive prisms. In some cases this can be avoided by choosing prism geometry which light enters and exits under perpendicular angle, by compensation through non-planar light trajectory, or by use of p-polarized light.

In contrast, spectacles with prisms of equal power for both eyes, called yoked prisms (also: conjugate prisms, ambient lenses or performance glasses) shift the visual field of both eyes to the same extent.[5]

Spectral dispersion is the best known property of optical prisms, although not the most frequent purpose of using optical prisms in practice.

Although, to the eye, the two fields of mechanics and optics seem to be quite different, it is interesting to note that there are many analogies between these two branches of science and each of these fields gains from the developments and understanding of the other and has tremendously contributed to the advancements in science and technology.

Prism spectacles with a single prism perform a relative displacement of the two eyes, thereby correcting eso-, exo, hyper- or hypotropia.

Hamilton’s principle of least action has given rise to the entire field of classical mechanics which then led to the development of quantum mechanics. The equivalent optics analogue, called the Fermat’s principle, is the basis of propagation of light in different media with non-uniform refractive index variations and can be used to explain the formation of mirages, light propagation through optical fibers (which form the backbone of the internet age), formation of images in the eye, etc.

Lens mirror and prism definitionpdf

In comparison with a usual glass substrate, the glass cube provides protection of the thin-film layer from both sides and better mechanical stability. The cube can also eliminate etalon effects, back-side reflection and slight beam deflection.

Similarities between the Schrodinger equation describing quantum phenomena and wave equation describing propagation of light waves lead to a number of mappings between mechanics and optics. Discrete energy states of quantum systems and discrete propagating modes of optical waveguides are a result of the same underlying physics and thus light propagation through waveguides can be used as nice visualization tools for better understanding of the abstract quantum picture.

An optical prism is a transparent optical element with flat, polished surfaces that are designed to refract light. At least one surface must be angled — elements with two parallel surfaces are not prisms. The most familiar type of optical prism is the triangular prism, which has a triangular base and rectangular sides. Not all optical prisms are geometric prisms, and not all geometric prisms would count as an optical prism. Prisms can be made from any material that is transparent to the wavelengths for which they are designed. Typical materials include glass, acrylic and fluorite.

Convexmirror

Various thin-film optical layers can be deposited on the hypotenuse of one right-angled prism, and cemented to another prism to form a beam-splitter cube. Overall optical performance of such a cube is determined by the thin layer.

Reflective prisms use total internal reflection to achieve near-perfect reflection of light that strikes the facets at a sufficiently oblique angle. Prisms are usually made of optical glass which, combined with anti-reflective coating of input and output facets, leads to significantly lower light loss than metallic mirrors.

A dispersive prism can be used to break white light up into its constituent spectral colors (the colors of the rainbow) to form a spectrum as described in the following section. Other types of prisms noted below can be used to reflect light, or to split light into components with different polarizations.

It was during this time that the famous Swiss mathematician Johann Bernoulli (1667-1748) posed the problem referred to as Brachistochrone problem (Brachistos: shortest; Chrone: time). This related to finding the curve connecting two points, at different heights, along which a body acted upon only by gravity will fall in the shortest time. This is similar to the problem of building a slide for a child that takes the child least time to descend to the bottom. Although this was a classic question in mechanics, Bernoulli used an analogous query in optics to solve the problem (based on the fact that, under certain situations, light takes least time to propagate between two points) and showed that the curve is a cycloid. The cycloid is a special kind of curve that has great practical significance in many areas including the design of roller coasters, emergency chutes in airplanes, ski slopes, etc. Not surprisingly, the cycloid appears on multiple occasions and is a very interesting curve that has been analyzed by many other scientists and engineers like Christiaan Huygens (1629-1695) who incidentally constructed the first pendulum clock, Blaise Pascal (1623-1662) and others.

Which statement is the best interpretation of the ray diagram shown

These are typically made of a birefringent crystalline material like calcite, but other materials like quartz and α-BBO may be necessary for UV applications, and others (MgF2, YVO4 and TiO2) will extend transmission farther into the infrared spectral range.

Reflective prisms are used to reflect light, in order to flip, invert, rotate, deviate or displace the light beam. They are typically used to erect the image in binoculars or single-lens reflex cameras – without the prisms the image would be upside down for the user.

which type ofmirrorhas a flat surface?

Total internal reflection alters only the mutual phase between s- and p-polarized light. Under well chosen angle of incidence, this phase is close to π / 4 {\displaystyle \pi /4} .

Surprisingly, in 1637 Fermat almost invented calculus, when he developed techniques to calculate areas (which is nothing but integral calculus), to determine maxima and minima of functions (differential calculus). The history of calculus is replete with arguments between Isaac Newton and Gottfried Wilhelm Leibniz (1646-1716), who had each in their teams, outstanding mathematicians supporting them.

Optics is the field dealing with imaging and propagation of light under various conditions and has helped build microscopes to see tiny objects and telescopes to see objects light years away. It has also been responsible for the birth of two of the greatest revolutions in science namely, the theory of relativity and quantum mechanics. The Greek philosophers were the first to try to explain the nature of light itself and Euclid (300 BC) was the first to state the various properties of light including the fact that light propagates along straight lines. A significant amount of work was carried out by various contributors to make spectacle lenses for correcting the eye, lenses for focussing sun light, etc.

Convexlens

By shifting corrective lenses off axis, images seen through them can be displaced in the same way that a prism displaces images. Eye care professionals use prisms, as well as lenses off axis, to treat various orthoptics problems:

Depolarization would not be observed for an ideal monochromatic plane wave, as actually both devices turn reduced temporal coherence or spatial coherence, respectively, of the beam into decoherence of its polarization components.

Mechanics, which deals with the motion of objects under the action of various forces, is one of the first of the exact sciences and is responsible for our understanding of the motion of planets and stars as well as terrestrial objects. Along with the theory of relativity, it forms the basis of many technologies including space flights, global positioning system, satellite communication, etc. After mathematics, mechanics is one of the oldest branches of science and has introduced concepts of force, energy, momentum, mass, heat and temperature. After the initial forays by Aristotle and other Greeks into explaining celestial phenomena, it was Nicolaus Copernicus (1473-1543) who placed the sun at the center of the solar system. He was followed by Galileo Galilei (1564-1642), who carried out beautiful experiments to understand the motion of objects, trying to generalize observations, and finally, Isaac Newton (1643-1727), who formulated the well-known laws of motion, which is today, the subject of school physics.

It was way back in 300 BC that Euclid made first note of the law of reflection about the angles of incidence and reflection to be equal. Then, in first century AD, Hero of Alexandria (10-70) proposed that the law of reflection is a consequence of the path travelled to be a minimum. Following this, there were a series of inputs from numerous polymaths including Ptolemy (100-170) , Ibn Sahl (940-1000), Ibn al Haytham (965-1040), Johannes Kepler (1571-1630), Willebrord Snell (1580-1626) and Rene Descartes (1596-1650), that augmented our understanding. In fact, Descartes used mechanical models to derive the laws of reflection and refraction. As our comprehension improved, Pierre de Fermat (1607-1665), helped formulate a clearer appreciation and in 1662, proposed that the path of light rays must correspond to that path that takes the minimum time. Today, the law for propagation of light is described and elaborated in terms of stationary paths where the light ray can take minimum time, maximum time or the same time, for nearby paths. This raises questions such as “how does light know at the beginning of its journey, which is the path that it should follow”, leading to teleological discussions. To quote Richard Feynman, “But the principle of least time is a completely different philosophical principle about the way nature works. Instead of saying it is a causal thing, that when we do one thing, something else happens, and so on, it says this: we set up the situation, and light decides which is the shortest time, or the extreme one, and chooses the path. But what does it do, how does it find out? Does it smell the nearby paths, and check them against each other? The answer is, yes, it does, in a way,” (Ref: Lectures in Physics, Feynman et al. 1964). It is insightful to observe that Fermat’s principle could explain the laws of reflection and refraction of light, and thus enabled a grasp of the concept, eventually leading to the design of instruments that are commonplace now, including microscopes and telescopes.

Another class is formed by polarizing prisms which use birefringence to split a beam of light into components of varying polarization. In the visible and UV regions, they have very low losses and their extinction ratio typically exceeds 10 5 : 1 {\displaystyle 10^{5}:1} , which is superior to other types of polarizers. They may or may not employ total internal reflection;