In the past, correcting spherical aberration required the combination of many different lens elements, and so the invention of aspherical lenses enabled a substantial reduction in the overall number of elements required for optical instruments.

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The larger the mirror of an astronomical telescope, the greater will be the telescope's ability to collect light. The primary mirror of the Subaru telescope, built by Japan's National Astronomical Observatory, has a diameter of 8.2 m, making Subaru the world's largest optical telescope, and one that boasts very high resolution, with a diffraction limit of only 0.23 arc seconds. This is good enough resolution to be able to make out a small coin placed on the tip of Mt. Fuji from as far away as Tokyo. Moreover, the Subaru telescope is about 600 million times more sensitive to light than the human eye. Even the largest telescopes until Subaru were unable to observe stars more than about one billion light years away, but Subaru can pick up light from galaxies lying 15 billion light years away. Light from 15 billion light years away and beyond is, in fact, thought to be light produced by the "big bang" that supposedly gave birth to the universe.

For a linearly polarized electromagnetic wave traveling in the x-direction, the angle the electric field makes with the y-axis is unique.

A polarizer produces linearly polarized light.  It is often convenient to orient the transmission axis of a polarizer vertically or horizontally to produce light with vertical or horizontal linear polarization.

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When unpolarized light is incident on a boundary between two dielectric surfaces, for example on an air-water boundary, then the reflected and transmitted components are partially polarized.  The reflected wave is 100% linearly polarized when the incident angle is equal to an angle called the Brewster angle.  For water this angle is is ~53o with respect to the normal or 37o with respect to the water surface. For are considerable angular range around the Brewster angle the reflected light is highly polarized in the horizontal direction.

When unpolarized light passes through a polarizer, the intensity is reduced by a factor of ½.  The average of cos2θ, averages over all angles θ is ½. Itransmitted = I0all angles = ½I0.

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Adding a further two pairs of convex/concave lenses and a mechanism for adjusting the distance between the single convex and concave lenses enables the modification of magnification over a continuous range. This is how zoom lenses work.

Concave lenses are used in eyeglasses that correct nearsightedness. Because the distance between the eye's lens and retina in nearsighted people is longer than it should be, such people are unable to make out distant objects clearly. Placing concave lenses in front of a nearsighted eye reduces the refraction of light and lengthens the focal length so that the image is formed on the retina.

An ideal polarizer is a material that passes only EM waves for which the electric field vector is parallel to its transmission axis.  The electric field is a vector and can be written in terms of the components parallel and perpendicular to the polarizer's transmission axis.  E = Eparallel + Eperpendicular.  An ideal polarizer passes Eparallel and absorbs Eperpendicular.If E0 is the incident field vector and the angle between E0 and the transmission axis is θ, then the magnitude of transmitted field vector is E0 cosθ and its direction is the direction of the transmission axis.  The intensity I of an electromagnetic wave is proportional to the square of the magnitude of the electric field vector.  We therefore haveItransmitted = I0 cos2θ. This is called the law of Malus.  If θ = 90o the transmitted intensity is zero.

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With a diameter of 52 cm and total weight of 170 kg, this high-precision lens unit is the fruit of Canon's lens design and manufacturing technologies. Stellar light picked up by the world's largest mirror and passed through this unit is focused on a giant CCD unit consisting of ten 4,096 x 2,048 pixel CCDs, producing images of 80 megapixels.

A beam of unpolarized light of intensity I0 passes through a series of ideal polarizing filters with their transmission axis turned to various angles, as shown in the figure. (a)  What is the light intensity (in terms of I0) in regions A, B, and C? (b)  If we remove the middle filter, what will be the light intensity at point C?

Because of the way in which lenses refract light that strikes them, they are used to concentrate or disperse light. Light entering a lens can be altered in many different ways according, for example, to the composition, size, thickness, curvature and combination of the lens used. Many different kinds of lenses are manufactured for use in such devices as cameras, telescopes, microscopes and eyeglasses. Copying machines, image scanners, optical fiber transponders and cutting-edge semiconductor production equipment are other more recent devices in which the ability of lenses to diffuse or condense light is put to use.

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Most optical devices make use of not just one lens, but of a combination of convex and concave lenses. For example, combining a single convex lens with a single concave lens enables distant objects to be seen in more detail. This is because the light condensed by the convex lens is once more refracted into parallel light by the concave lens. This arrangement made possible the Galilean telescope, named after its 17th century inventor, Galileo. Adding a second convex lens to this combination produces a simple telephoto lens, with the front convex and concave lens serving to magnify the image, while the rear convex lens condenses it.

There are four other key types of aberration: spherical and coma aberration, astigmatism, curvature of field, and distortion. Together with chromatic aberration, these phenomena make up what are known as Seidel's five aberrations. Spherical aberration refers to the blurring that occurs as a result of light passing through the periphery of the lens converging at a point closer to the lens than light passing through the center. Spherical aberration is unavoidable in a single spherical lens, and so aspherical lenses, whose curvature is slightly modified towards the periphery, were developed to reduce it.

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Convex lenses are used in eyeglasses for correcting farsightedness, where the distance between the eye's lens and retina is too short, as a result of which the focal point lies behind the retina. Eyeglasses with convex lenses increase refraction, and accordingly reduce the focal length.

When the sun is at a low angle in the sky, the sunlight reflecting off the surface of water is nearly 100% horizontally polarized because the angle of incidence is close to the Brewster angle. Glare-reducing sunglasses are coated with a polarizer with a vertical transmission axis and therefore block the reflected light.

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Optically active or circular birefringent materials rotate the direction of polarization of linearly polarized light.  The amount of rotation depends on the wavelength of the light.  Sugar molecules have a handedness (chirality) and in solution are optically active.  If we polarize white light and pass it through sugar syrup, the direction of polarization of the light emerging from the syrup will be different for the different color components.  If the light then passes through a second polarizer, its color changes with the orientation of the transmission axis of this polarizer.

Special lenses, known as fluorite lenses, and boasting very low dispersion of light, have been developed to resolve the issue of chromatic aberration. Fluorite is actually calcium fluoride (CaF2), crystals of which exist naturally. Towards the end of the 1960s, Canon developed the technology for artificially creating fluorite crystals, and in the latter half of the 1970s we achieved the first UD (Ultra Low Dispersion) lenses incorporating low-dispersion optical glass. In the 1990s, we further improved this technology to create Super UD lenses. A mixture of fluorite, UD and Super UD elements are used in today's EF series telephoto lenses.

Chromatic aberration caused by diffraction on the one hand, and refraction on the other arise in completely opposite ways. Skillful exploitation of this fact enables the creation of small and light telephoto lenses. Unlike pickup lenses for CD and DVD players, incorporating simple diffractive optical elements into SLR camera lenses results in the generation of stray light. However this problem can be resolved by using laminated diffractive optical elements, in which two diffractive optical elements are aligned within a precision of a few micrometers.

Subaru's primary focus camera boasts a very wide field of view of 30 minutes, which is equivalent to the diameter of the full moon as seen from earth, enabling Subaru to make not only very precise, but also speedy observations of the heavens. The only telescope in the world equipped with a glass primary mirror of 8 m in diameter, Subaru is a powerful aid to research on the birth of galaxies and the structure of the universe. Previously, structural considerations prevented heavy optical systems from being placed on top of the primary focus of large reflecting telescopes. This problem was overcome by the development of a smaller and lighter prime focus corrector lens optical system, comprising seven large lens elements in five groups.

The focused image through a single convex lens is actually very slightly distorted or blurred in a phenomenon known as lens aberration. The reason why camera and microscope lenses combine so many lens elements is to correct this aberration to obtain sharp and faithful images. One common lens aberration is chromatic aberration. Ordinary light is a mixture of light of many different colors, i.e. wavelengths. Because the refractive index of glass to light differs according to its color or wavelength, the position in which the image is formed differs according to color, creating a blurring of colors. This chromatic aberration can be canceled out by combining convex and concave lenses of different refractive indices.

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Polarization is a phenomenon peculiar to transverse waves.  Longitudinal waves such as sound cannot be polarized.  Light and other electromagnetic waves are transverse waves made up of mutually perpendicular, fluctuating electric and magnetic fields.  In the diagram below an EM wave is propagating in the x-direction, the electric field oscillates in the xy-plane, and the magnetic field oscillates in the xz-plane.  A line traces out the electric field vector as the wave propagates.

There are different polarization mechanisms.  The most common method of producing polarized light is to use polaroid material, made from chains of organic molecules, which are anisotropic in shape.  Light transmitted is linearly polarized perpendicular to the direction of the chains.  The transmission axis is perpendicular to the chains.

The word "lens" owes its origin to the Latin word for lentils, the tiny beans that have from ancient times been an important ingredient in the cuisine of the Mediterranean region. The convex shape of lentils resulted in thier Latin name being coined for glass possessing the same shape.

Lenses may be divided broadly into two main types: convex and concave. Lenses that are thicker at their centers than at their edges are convex, while those that are thicker around their edges are concave. A light beam passing through a convex lens is focused by the lens on a point on the other side of the lens. This point is called the focal point. In the case of concave lenses, which diverge rather than condense light beams, the focal point lies in front of the lens, and is the point on the axis of the incoming light from which the spread light beam through the lens appears to originate.

Certain birefringent crystalline substances bend light trough an angle that depends upon the state of incident polarization.  The have an optic axis.  Unpolarized light entering a birefringent crystal not along the optic axis of the crystal is split into beams which are bend by different amounts.

If this arrangement is then combined with a refractive convex lens, chromatic aberration can be corrected. Smaller and lighter than the purely refractive lenses that have been commonly used until now, these diffractive lenses are now being increasingly used by sports and news photographers.

An unpolarized electromagnetic wave traveling in the x-direction is a superposition of many waves.  For each of these waves the electric field vector is perpendicular to the x-axis, but the angle it makes with the y-axis is different for different waves.  For unpolarized light traveling in the x-direction Ey and Ez are randomly varying on a timescale that is much shorter than that needed for observation.

Some materials turn birefringent when stressed.  By placing transparent materials between two polarizers, we can perform stress analysis tests.

Because light is a wave, when it passes through a small hole, it is diffracted outwards towards shadow areas. This phenomenon can be used to advantage to control the direction of light by making concentric sawtooth-shaped grooves in the surface of a lens. Such lenses are known as diffractive optical elements. These elements are ideal for the small and light lenses that focus the laser beams used in CD and DVD players. Because the lasers used in electronic devices produce light of a single wavelength, a single-layer diffractive optical element is sufficient to achieve accurate light condensation.