If a point object is placed on the axis of the large lens, images I p and I m will be formed by the paraxial and marginal rays respectively.
The paraxial rays of light from the image at a longer distance from the lens than the marginal rays. The image is not sharp at any point on the axis.
If the screen is placed perpendicular to the axis at AB, the image appears to be a circular patch of diameter AB. The patch of diameter AB is called the circle of least confusion and corresponds to the position of the best image. The distance I m I p measures the longitudinal spherical aberration and the radius of the circle of least confusion measures the lateral spherical aberration. When the aperture of the lens is relatively large compared to the focal length of the lens, the cones of the rays of light refracted through different zones of the lens surface are not brought to focus at the same point on the axis.
The marginal rays come to focus at a nearer point I m and the paraxial rays come to focus at a farther point I p. Thus for point object O on the axis, the image extends over the length I m I p. This effect is called spherical aberration and arises due to the fact that different annular zones have different focal lengths. The spherical aberration produced by a concave lens is shown in the figure. It is positive for the convex lens and negative for the concave lens, both paraxial and marginal rays cannot focus at a single point.
The rays incident on the lens near the principal axis are called paraxial rays and the rays falling near the edge are called marginal rays. For a single lens, spherical aberration cannot be entirely eliminated. However, it can be reduced by following methods:. When an electromagnetic radiation is an incident on an electric charge at rest, the charges particle accelerates along the direction of the electric field of the incident radiation. Since the electric charge is at rest, it does not experience any force due to magnetic field of the electromagnetic radiations in all the directions, and this process is called scattering.
The scattering of light by the matter and he found that the intensity of a particular wavelength of the scattered light depends on its wavelength. Lord Rayleigh found that the intensity of the light corresponding to a wavelength of the scattered light varies inversely as the fourth power of the wavelength.
Since, the wavelength of the blue colour is approximately half the wavelength of red colour, the scattering of blue light is about 2 4 times i. Due to this, blue colour predominates and the sky appears blue. Find Your Query. Syllabus Mechanics. Heat and Thermodynamics. Geometrical Optics. Overview This note provides us an information about a spherical aberration in a lens and scattering of light.
If a point object is placed on the axis of the large lens, images Ip and Im will be formed by the paraxial and marginal rays respectively. Note Things to remember. Spherical Aberration in a Lens and Scattering of Light Spherical Aberration in a Lens If a point object is placed on the axis of the large lens, images I p and I m will be formed by the paraxial and marginal rays respectively. Things to remember Spherical aberration can be reduced either by cutting off the paraxial rays or by cutting off the marginal rays.
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Plano-convex lenses only reduce the spherical aberration if they are used in the appropriate position with respect to the conjugates. To understand this, one intuitive explanation is this: Snell's law is not linear, so it does not behave proportionately for large versus small angles. Looking at the two lenses below, for the left hand lens the angles of deviation for the marginal ray the ray at the edge of the lens are distributed between the front and back surfaces.
For the right hand lens, the 2nd surface performs all of the work of refraction. It turns out the right hand lens will have much more spherical aberration than the left hand lens, when used in this manner. This is a simplified example, but more complicated lenses are designed by adjusting the amount of refraction at each surface, ideally so that aberrations on one surface are compensated by aberrations on another surface.
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Plano-Convex Spherical Lenses
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It only takes a minute to sign up. As I understand, less spherical aberration is obtained when a collimated beam is focused with a plano-convex lens as opposed to a biconvex lens. What would be a situation when a bi-convex lens should be used?
When should one use a bi-convex lens vs a plano-convex lens? To elaborate on George's answer, a plano-convex lens is typically used in a telescope where both the beam coming in and the beam going out are collimated. If the lenses are oriented correctly this will produce less aberration than a bi-convex lens. In this case the correct orientation is to have the curved surfaces of the lens pointing out towards the collimated beams. Note that if the lenses are oriented the other waythen this arrangement will produce more spherical aberration than the bi-convex case.
To answer your question specifically, the bi-convex lens is the best lens to use in the situation where the beam incident on the lens is diverging and the beam leaving the lens is converging symmetrically. The idea to minimize spherical aberration when using spherical lenses is to trade-off between the two surfaces of the lens so that you show the beam the least curved surface, relative to the beams own curvature, at each refraction.
There is actually a whole class of lenses known as 'best form' lenses see e. Indeed, if you are willing to spend the money, you can do away with spherical aberration all together by using parabolic surfaces. Typically you can only get parabolic mirrors, however, not lenses.
In an application requiring very fast telescopes, this is the way to go. As a general rule, the arrangement that more closely equalizes the deviation at the two surfaces, will yield the smallest spherical aberration. That arrangement, minimizes the incidence angles and deviation at the two faces, and smaller incidence angles give less spherical aberration. So an equi bi-convex lens would work better in a 1:! The plano-convex will work better at infinity focus.
Sign up to join this community. The best answers are voted up and rise to the top.A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction.
A simple lens consists of a single piece of transparent materialwhile a compound lens consists of several simple lenses elementsusually arranged along a common axis. Lenses are made from materials such as glass or plasticand are ground and polished or molded to a desired shape. A lens can focus light to form an imageunlike a prismwhich refracts light without focusing.
Devices that similarly focus or disperse waves and radiation other than visible light are also called lenses, such as microwave lenses, electron lensesacoustic lenses, or explosive lenses.
The lentil plant also gives its name to a geometric figure. Some scholars argue that the archeological evidence indicates that there was widespread use of lenses in antiquity, spanning several millennia. The oldest certain reference to the use of lenses is from Aristophanes ' play The Clouds BC mentioning a burning-glass. Ptolemy 2nd century wrote a book on Opticswhich however survives only in the Latin translation of an incomplete and very poor Arabic translation.
The book was, however, received, by medieval scholars in the Islamic world, and commented upon by Ibn Sahl 10th centurywho was in turn improved upon by Alhazen Book of Optics11th century. The Arabic translation of Ptolemy's Optics became available in Latin translation in the 12th century Eugenius of Palermo Between the 11th and 13th century " reading stones " were invented.
These were primitive plano-convex lenses initially made by cutting a glass sphere in half. The medieval 11th or 12th century rock crystal Visby lenses may or may not have been intended for use as burning glasses.
Spectacles were invented as an improvement of the "reading stones" of the high medieval period in Northern Italy in the second half of the 13th century. With the invention of the telescope and microscope there was a great deal of experimentation with lens shapes in the 17th and early 18th centuries by those trying to correct chromatic errors seen in lenses.
Opticians tried to construct lenses of varying forms of curvature, wrongly assuming errors arose from defects in the spherical figure of their surfaces. This led to the invention of the compound achromatic lens by Chester Moore Hall in England inan invention also claimed by fellow Englishman John Dollond in a patent.
Most lenses are spherical lenses : their two surfaces are parts of the surfaces of spheres. Each surface can be convex bulging outwards from the lensconcave depressed into the lensor planar flat. The line joining the centres of the spheres making up the lens surfaces is called the axis of the lens. Typically the lens axis passes through the physical centre of the lens, because of the way they are manufactured.
Lenses may be cut or ground after manufacturing to give them a different shape or size. The lens axis may then not pass through the physical centre of the lens. Toric or sphero-cylindrical lenses have surfaces with two different radii of curvature in two orthogonal planes. They have a different focal power in different meridians.
This forms an astigmatic lens. An example is eyeglass lenses that are used to correct astigmatism in someone's eye. Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex or double convexor just convex if both surfaces are convex.
If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave or just concave. If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.
If the lens is biconvex or plano-convex, a collimated beam of light passing through the lens converges to a spot a focus behind the lens. In this case, the lens is called a positive or converging lens. For a thin lens in air, the distance from the lens to the spot is the focal length of the lens, which is commonly represented by f in diagrams and equations.
An extended hemispherical lens is a special type of plano-convex lens, in which the lens's curved surface is a full hemisphere and the lens is much thicker than the radius of curvature.Choose products to compare anywhere you see 'Add to Compare' or 'Compare' options displayed.
Optical Post Assemblies 0. Optical Pedestal Assemblies 1. Optical Post Assemblies 1. They can be used to focus, collect and collimate light. The asymmetry of these lenses minimizes spherical aberration in situations where the object and image are located at unequal distances from the lens. N-BK7 lenses are a great choice for most general purpose visible and NIR applications, featuring high homogeneity and low bubble and inclusion content. UV Fused Silica lenses are ideal for UV or higher energy applications, combining a very low thermal expansion coefficient and excellent transmittance down to nm.
For the highest energy applications, we offer high purity fused silica lenses. Plano-Convex lenses are the best choice for focusing parallel rays of light to a single point. Industrial Motion. Custom Motion Solutions. Vacuum Compatible Motorized Positioners. Optical Posts 0. Lab Supplies. Custom Component Solutions. Diffraction Gratings. Fiber Optics. Optic Accessories. Optic Sets. Custom Optics Solutions. Solar Cell Test Systems. Custom Vibration Isolation Solutions.
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