Mirror This is one of the most basic but most commonly used instruments today. It consists of a glass sheet silvered on one side, so as to facilitate maximum reflection of light falling on the other. It can either be plain, spherical or a combination of both. A plain mirror is one whose surface of reflection lies in one plane.

A spherical mirror can be obtained by taking a part of a glass sphere and silvering it on one side to as to allow reflection from the other side. The centre of the sphere of which the mirror is a part is known as the centre of curvature. The point at the middle of the mirror is known as its pole. Line joining the radius and the pole is the principal axis. The point on the principal axis through which all parallel rays, after reflection, pass (in a concave mirror) or seem to pass (in a convex mirror), is the focal point. Distance between the focal point and the pole is the focal length of the lens. It is half of the radius of curvature. The plane through the focal point and a perpendicular to the principal axis is the focal plane. A ray close to the principal axis is called a paraxial ray. Convex and concave mirrors form images of different nature depending upon the position of the object before the mirror. For a spherical mirror, the object distance (u), image distance (v) and the focal length(f) are related by the formula 1/u +1/v = 1/f The magnification produced by a mirror is given by m = -(v/u) Plain and concave mirrors are used as looking glasses in houses. Convex mirrors are commonly used in vehicles. Other applications of mirrors are in fields like astronomy, geography and sciences.

Lens It is one of the most familiar optical devices to the human being. We have a lens in our eye, and use many other types in daily life. A lens is a transparent material bound by two spherical surfaces, which determine the type of the lens.

It can either be bi-convex, bi-concave, plano-convex, plano-concave or a combination of both convex and concave. Thin lenses are those whose thickness is negligible as compared to other objects around. Hence, linear displacement due to refraction can be neglected in them. A lens has two focal points, one for each surface.

Depending upon the position of the object, the nature of the image formed is different. For a convex lens, there are six cases: Case 1: Object at infinity. Image is formed at focus on the other side, is real and diminished. Case 2: Object beyond centre of curvature. Image is formed between focus and centre of curvature on the other side, is real, diminished and erect. Case 3: Object at centre of curvature. Image is formed at centre of curvature on the other side, is real, diminished and inverted. Case 4: Object between centre of curvature and focus. Image is formed beyond centre of curvature on the other side, is real, magnified and inverted. Case 5: Object at focus. Image is formed at infinity on the other side, is real, inverted and highly magnified. Case 6: Object between pole and focus. Image is formed on the same side, is virtual, magnified and erect.

For all finite positions of an object before a convex lens, a virtual, diminished and erect image is formed between focus and the pole.

Lens Maker's Formula This formula relates the focal length of the lens to the radius of curvature. It is given by: 1/f = (: - 1) (1/R1 - 1/R2) where, f is the desired focal length of the lens, : is the refractive index of the material being used and R1 and R2 are the radi of curvature of the two refracting surfaces. The above expression can also be expresses as the lens formula: 1/f = 1/v - 1/u where, v is the image distance and u is the object distance.

Power of a lens This is defined as the inverse of its focal length, i.e. for a lens with focal length f, the power is expressed by P = 1/f

Two thin lenses separated by a distance For two different lenses of focal lengths, f1 and f2, separated by a distance d, the resultant focal length F is given by: 1/F = 1/f1 + 1/f2 - d/(f1f2) The distance s of an equivalent lens from the one with focal length f2 s given by: s = dF / f1

Telescope This instrument is used to view distant objects that are not vivible to the naked eye. It is not quite clear as to who was the inventor of the first telescope, although it is said that the use of lenses for a telescope was started by a Dutch spectacle-maker, Lippershey and his assistant in 1608. Other people however, have also staked the claim of being inventors of this instrument.

The first telecopes consisted of two refracting lenses which were used to bend light, one with larger focal length at one end and another at the other end as the eyepiece. One of the earliest inventors of telescopes was Galileo, whose telescope consisted of a convex objective lens and a concave eyepiece lens. In his book, Sidereus Nuncius, he challenged the strongest beliefs about the universe at that time. Reflecting telescopes later came into scene, Newton being one of the first to invent them. His telescope however, did not work well, as it was quite small, and its mirrors tarnished quickly.

Three types of telescopes are in use today: Astronomical: magnifying power given by m = - (f0/fe) (1 + fe/D) Terrestrial: magnification given by m = (f0/fe) (1 + fe/D) Galilean: angular magnification power given by m = - (f0/fe) (1 + fe/D) In all the three cases, and are the focal lengths of the objective and the eyepiece lenses, and D is the distance between the image and the pole of the eyepiece lens.

Microscope A microscope is used to view tiny things, that the human eyes cannnot see, observe and analyse. One of the first inventors of microscopes was Antony Leeuwenhoek, whose microscope consisted of a single convex lens, fixed between two metal plates. The object to be viewed was placed on a pin and moved by a system of screws to bring it into focus.

Compund microscopes are said to be invented towards the end of the 16th century by Zacharias Jansses. Many years later, an Englishman by the name of Robert Hooke, published a book called Micrographia, which contained drawings of minute bodies which he had observed under his microscope. It was a compound microscope which contained two to three lenses. A modern compound microscope can work with a minimum of just two lenses, one of which is a small, but powerful objective lens and the other a larger eyepiece lens. Light from the specimen is focussed by the objective lens so that it forms a magnified real image, which is then enlarged by the eyepiece lens, from where it reaches the human eye. Electron microscopes were introduced in the last century. They use beams of electrons bent by strong magnetic fields instead of a simple light waves.

The magnifying power of a microscope with f1 and f2 as the focal lengths of the objective and the eyepiece lenses respectively, d being the value for the near point of the eye, is given by: m = - (1/f1) (d/f2) - for normal adjustment; and m = - (1/f1) (1 + d/f2) - for the adjustment of the final image at the least distance of clear vision

Prism It is a pyramidal piece of a refracting material that can produce a spectrum when white light passes through it. A typical prism has just two refracting surfaces, whuch are inclined to wach other by an angle of 2 known as the angle of the prism. A ray incident on one surface of a simple prism with angle i, emerges at an angle i' given by: * = i + i' - 2, * being the angle of deviation.

Periscope A periscope is an instrument that is used to see over barriers. A simple periscope consists of a double twisted tube, with two mirrors placed at each of its corners, so as to allow the reflection of light entering the instrument at one end of the tube at make it emerge from the other end. Mirrors in modern telescopes have been replaced by total reflecting prisms, since the fraction of reflected light is more during total internal reflection than in reflection from the surface of a mirror. Periscopes are most commonly used today in submarines to have a view of the surface of the ocean or sea the submarine is in.

Kaleideoscope This is a simple and easy-to-construct instrument, which is used to produce beautiful patterns, and hence has applications in the design industry. It consits of a number of rectangular plane mirrors, joined together to form a tube, of polygonal cross-section. One end is covered with another plane mirror, and the other by a transparent material after introducing some broken pieces of coloured glass into the tube. When observed from the transparent side, beautiful patterns are seen on the other side due to multiple reflection by the mirrors.

Spectrometer This instrument is used to produce and study the pure spectrum in the visible region, and consists of three parts: 1). Collimator: A long cylindrical tube fitted with an achromatic converging lens with shorter tube inside it having a linear slit at the outer end. It is used to make the light parallel before dispersion. 2). Prism table: A horizontal platform, with a dispersing element placed on it. It can be rotated about its axis, and has a horizontal graduated circular scale which moves with it. 3). Telescope: An astronomical telescope with a vernier scale that rotates on the horizontal circular scale when it is rotated. These parts are fitted together in a compact unit and can be adjusted separately to receive light waves of different wavelengths at dfferent angular positions of the telescope. A spectrometer can be used to measure the angle of a prism, the angle of minimum deviaiton and variation of its refractive index with wavelength.

Optical fibres These are very thin fibres made of glass or plastic with a radius of the order of a micrometer. A bundle of optical fibres separated by an insulating material denser than that of the fibre is known as a "light pipe" can can be used to transmit data, which is equivalent to that transmitted by an enormous number of electric cables. Light enters at one end of the optical fibre, and hits the inner wall at an incident angle which is more than the critical angle due to the thin radius. Light pipes can be used to carry tremendous amout of information in the form of electric pulses and radio siganls. They are being used by doctors to see the inside of the human body with the help of an endoscope.