Ray tracing allows us to get a qualitative picture of image formation. The following formula, called the lensmaker equation, is used to determine whether a lens will behave as a converging or diverging lens based on the curvature of its faces and the relative indices of the lens material n 1 and the surrounding medium n 2. Lensmakers equation wolfram demonstrations project. Apr 28, 2019 numerical methods in lens a lens formula definition. Lens makers equation light rays from a beam source, initially in air, are incident on a material of different index of refraction position is given in centimeters. Lens makers formula and limitations of lens makers. Calculate the position of the images formed by the fol lowing concave. Suppose a thin lens immersed in air is made from a material with index of refraction, n.
The camera uses a converging lens whose focal length is 0. Derivation of lens maker formula for concave mirror ask questions, doubts, problems and we will help you. Commonly it is given in the thin lens limit, where it is assumed that the thickness of the lens is small compared to the object and image distances. Consider a convex lens or concave lens of absolute refractive index m 2 to be placed in a rarer medium of absolute refractive index m 1 considering the refraction of a point object on the surface xp 1 y, the image is formed at i 1 who is at a distance of v 1 ci 1 p 1 i 1 v 1 as the lens is thin. Lenses of different focal length are used for different optical instruments. Lenses of different focal lengths are used for various optical instruments. The virtual image formed by a diverging lens an object is placed 7. The radius r2 is negative since it extends left from the second surface. A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction.
Lens makers formula and lens formula and magnification. The focal length of the lens is given by the lens makers equation. Hey guys, in this video were going to talk about something called the lens maker equation which is the equation that will tell us the focal length of a thin lens based on the shape of the two pieces of glass that make it up. Is the 1f term in the lens makers equation the same as the 1f term in the thin lens equation and hence, equal to power. The lensmakers equation relates the focal length of a simple lens with the spherical curvature of its two faces.
For more information on and versions of the lens makers equation, please see the lens makers equation calculator page. The lensmakers equation links the radii of curvature of two sides of a lens, the refractive index of the material from which it is made and the focal length of the lens. The derivation of the gaussian form proceeds from triangle geometry. The sign of is determined by the location of the center of curvature along the optic axis, with the origin at the center of the lens. In this video learn how to derive lens maker formula for thin lens. Rays of light entering a converging lens parallel to its axis converge at its focal point f. Focal length for a lens the focal length of a lens is related to the curvature of its front and back surfaces and the index of refraction of the material 1 the lens makers equation 1 f n 1 1 r 1 r 2. For a double convex lens the radius r1 is positive since it is measured from the front surface and extends right to the center of curvature. This equation is used for determining the focal length of a thin lens thickness 0 with radii of curvature r1 and r2. The lens makers equation will tell us which shapes are which.
At any point along the optical train an optical axis is defined corresponding to a central ray. Notes on lens makers formula and combination of thin lenses. These equations, called the thinlens equation and the lens makers equation, allow us to quantitatively analyze thin lenses. The lens makers formula can be derived for a concave lens in the same way.
Commonly it is given in the thinlens limit, where it is assumed that the thickness of the lens is small compared to the object and image distances. Derive a generalized lens makers equation to replace the equation 1fn. The thin lens equation is also sometimes expressed in the newtonian form. So to derive the lens makers formula, you first need to derive the relation between object and image distance in terms of refractive index of the medium and the. The lens maker s formula can be derived for a concave lens in the same way. For the love of physics walter lewin may 16, 2011 duration. If the lens is biconvex or planoconvex, a collimated beam of light passing through the lens will be converged or focused to a spot behind. Since ray strikes surface normally, it must return to the same point. Ece 5616 curtis real surfaces refractive via fermats principle calculate optical path length. Notes, exercises, videos, tests and things to remember on lens makers formula and combination of thin lenses. The focal length of a lens depends on the refractive index of the lens and the radii of curvature. The derivation of equation 34 is straightforward, but a bit tedious. In order for the equipment to operate correctly this focal length must be strictly adhered to. For lens in close contact, the power of the combined lens is equal to the sum of their individual lens powers.
Using the lens makers equation 3 and the appropriate sign for radii r1 and r2, determine the formulae for the focal distance of the hemisphere and the sphere in terms of r and n. Lensmakers equation links the radii of curvature of two sides of a lens, the refractive index of the material from which it is made and the focal length of the lens. Thin lenses and optical instruments equipment 1 meter optical bench with 5 moveable mounts, lighted test object, 3 lens holders, screen, 2 short focal length double convex lenses l1, e1, 2 medium focal length double convex lenses l2 and l3, 1 long focal length double convex lens l4, 1 double concave lens l5. Question regarding lens makers equation and thin lens equation. Jan 21, 2014 for the love of physics walter lewin may 16, 2011 duration. Thin lens and lens maker equations physics video clutch prep. A simple lens consists of a single piece of material, while a compound lens consists of several simple lenses elements, usually along a common axis. Numerical methods in lens a lens formula definition. Lenses are made from materials such as glass or plastic, and are ground and polished or molded to a. Take convex lens with absolute refractive index in rarer medium. The lens maker s formula indicates that a convex lens can behave like a diverging one if m 1 m 2 i. Lenses were probably used as magnifying glasses, or as a burningglass to. One side of the lens has radius of curvature, r 1, and the other side has a radius of curvature, r 2. What must the focal length of a thin lens be if it is to be placed in close combination with a 2diopter lens to form a combination lens that has a focal length of.
The distance from the center of the lens to the focal point is the lenss focal length f. Small angles are made by incident and refracted ray. The ray tracing technique is based on two reference planes, called the input and output planes, each perpendicular to the optical axis of the system. Derive a generalized lens makers equation to replace the equation when the lens is surrounded by a medium other than air. A lens is a transmissive optical device which affects the focusing of a light beam through refraction.
The lens maker formula is commonly used by lens manufacturers for manufacturing lenses of desired focal length. We assume a thin, converging lens and that the light rays we are dealing with are close to the principal axis and make very small angles with the principal axis angles of less than 10 o, resulting in very small angles of incidence. How to determine if r1 and r2 for a lens is negative or positive. The focal length of a lens depends upon the refractive index of the material of the lens and the radii of curvatures of the two surfaces. Real surfaces reflective derive power of mirror by placing object at center of curvature.
The focal length of a lens depends upon the refractive. Derive a generalized lens maker s equation to replace the equation 1fn. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses elements, usually arranged along a common axis. Remember that by our sign convention, r lens power which is positive. The attempt at a solution i used three equations to derive the upper equation. However, if the medium on both sides of the lens has the same index of refraction, which is the case if the lens is in air, the two focal lengths are equal. Derivation of lens maker formula detailed lens maker. It is used for determining the focal length of a thin lens thickness 0 with radii of curvature r1 and r2. For more information on and versions of the lens maker s equation, please see the lens maker s equation calculator page. A certain piece of equipment contains a lens, made of glass n 1. So extending left is negative, extending right is positive, correct.
Check the limitations of the lens maker s formula to understand the lens maker formula derivation is a better way. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces. This lens makers equation 1 solved for r 1 r 1 calculates the radius of curvature of the objectfacing side of a lens given its geometry and surroundings. Check the limitations of the lens makers formula to understand the lens maker formula derivation is a better way. We will start with reflection of light and spherical mirrors and gradually proceed to cover advanced topics such as refraction, prisms, total internal reflection, and optical instruments. Let r 1 and r 2 be the radii of curvature of two spherical surfaces acb and adb respectively and p be the optic centre. Refer to the following information for the next two questions. The lens makers derivation assumes some condition, they are. I sometimes have trouble knowing when to use either of these equations in predicting focal length, object length, image length. You can change the curvature of the surface of the material as well as the index of refraction. The equations are also correct when the lens are immersed in any medium, provided that n is interpreted as the relative index of the material of the lens with respect to the medium. It is a relation that connects the focal length of a lens to radii of curvature of the two surfaces of the lens and the refractive index of the material of the lens. Paraxial into real surfaces curvature, radius power lens and mirrors lens maker equation mirror and lens in contact principle planes. Thin lenses and optical instruments university of calgary.
The lens is thin so that distances measured from the poles of its surfaces can be taken as equal to the distances from the optical centre of the lens. The lens makers formula indicates that a convex lens can behave like a diverging one if m 1 m 2 i. The derivation of lens maker formula is provided here so that aspirants can understand the concept more effectively. Lens manufacturers use the lens makers formula to manufacture lenses of the desired focal length. Use the lensmakers equation to determine the focal length of a thin lens. Now, the change in direction or bending of a light wave passing from one transparent medium to another caused by the change in waves speed is the refraction. In this video tutorial, we will learn the fundamental concepts of ray optics and understand how light is reflected, absorbed, and transmitted. Let r 1 and r 2 be the radii of curvature of two spherical surfaces acb and adb respectively and p be the optic centre consider a point object o on the principal axis. The thin lens equation and the magnification equation example. As b and d both are close to the optical centre of the lens, bo. O c 1 ii c 2 1 p 1 p 2 i2 b e a d u1 v1 v2 r1 r2 t n1 t. Given descartes formula for a thin lens, derive the lens makers formula and the thin lens equation. For a thin lens, the lens power p is the sum of the surface powers.
A lens maker formula may be defined as the formula which gives the. Let us consider a thin lens made up of a medium of refractive index. Thin lens is used for measure the distance from surface poles to lens optical centre distance. Onsider a lens having index of refraction n2 and s. Nov 06, 2019 this lens maker s equation 1 solved for r 1 r 1 calculates the radius of curvature of the objectfacing side of a lens given its geometry and surroundings. Is the 1f term in the lens maker s equation the same as the 1f term in the thin lens equation and hence, equal to power. Once you have these equations, you should be able to find n from the. Normally, the thickness of the lens must be considered. Ray diagrams for thin lenses three rays are drawn the first ray is drawn parallel to the first. The equation derived for a thin lens and relating two conjugated points is. Lensmaker equation calculator, calculate lens focal length. To obtain numeric information, we derive a pair of equations from a geometric analysis of ray tracing for thin lenses.
Lensmaker equation is used to determine whether a lens will behave as a converging or diverging lens based on the curvature of its faces and the relative indices of the lens material and the surrounding medium. A radius of curvature is positive when its center of curvature lies to the right of the surface, and negative when its center of curvatures lies to the left of the surface. Let us now see the refraction of light at the spherical surface. Lensmakers equation for thick lens in two different media. The thinlens equation and the magnification equation example.
The equation relating the object distance u, the image distance v and the focal length f of the lens is called the lens formula. Question regarding lens makers equation and thin lens. Be careful with the sign of the focal length in the lens formula. The oldest lens artifact is the nimrud lens, which is over three thousand years old, dating back to ancient assyria. Physics 212 and 222 lenses properties of thin lenses lens. The lens equation essentially states that the magnification of the object distance of the image over distance of the object. Using the lens maker s equation 3 and the appropriate sign for radii r1 and r2, determine the formulae for the focal distance of the hemisphere and the sphere in terms of r and n.
474 188 720 412 1593 518 1254 1219 1013 560 226 609 1545 1239 615 496 1476 934 948 284 715 238 1375 1146 1101 75 765 14 702 524 603 868 877 390 1268 1369 408 1273 1455 1141 903 910 388