The equation relating the object distance u, the image distance v and the focal length f of the lens is called the lens formula. Let c 1 and c 2 be the centre of curvature of the two spherical surfaces. Remember that by our sign convention, r derivation of lens maker formula is provided here so that aspirants can understand the concept more effectively. The focal length of a lens depends upon the refractive. 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. Could someone link a derivation of the thick lens equation so i could figure it out myself. If a lens is thicker than that measure, the thin lens equation cannot be used. 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 formula is commonly used by lens manufacturers for manufacturing lenses of desired focal length. Since ray strikes surface normally, it must return to the same point. A lens maker formula may be defined as the formula which gives the. Some people thought that magnification was the sole contributor to resolution. For a thin lens, the power is approximately the sum of the surface powers the radii of curvature here are measured according to the cartesian sign convention. Lens makers formula example consider a convex lens or concave lens of absolute refractive index.
Consider the thick biconvex lens shown in figure \\pageindex8\. A point source lies on the optical axis of the lens, a distance u away from the centre of the lens. Applying the equation of paraxial refraction with air to each surface gives 1 2 using, 3 adding 1 and 3 gives 4 for conjugate points, 5 as is derived by morgan, 6 the ends of the lens are at 7 8 morgan, j. Lens makers formula definition, examples, diagrams. It follows from the refraction due to convex spherical surface xp 1y. Considering the refraction of a point object on the surface x p 1 y, the image is formed at i 1 who is at a distance of v 1. Lens design is quite complex, involving compromises on many parameters and design for manufacturing considerations. In figure pc 1 r 1 is normal at p and oc 2 r 2 normal at q where c 1 and c 2 are centre of curvature of lens surfaces. If you want me to teach you biology or chemistry or physics. Numerical methods in lens a lens formula definition. These equations, called the thinlens equation and the lens makers equation, allow us to quantitatively analyze thin lenses.
Real surfaces reflective derive power of mirror by placing object at center of curvature. Since the angle between two tangents forming a prism is equal to the angle between two radii, so we have. The refracted ray from a suffers a second refraction on the surface xp 2y and emerges along bi. 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. Please note the following so you can understand how the thin len equation can be derived. A beam of light from the source moves towards the lens at an angle. Due to the geometrical symmetry, the thin lens equation can be used for a convex and concave mirrors.
Everyone wants to explain but not many have the talent, but i have it. O c 1 ii c 2 1 p 1 p 2 i2 b e a d u1 v1 v2 r1 r2 t n1 t. Lens makers formula is the relation between the focal length of a lens to the refractive index of its material and the radii of. This derivation is not fundamental, but it is more intuitive. 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. Rays incident on the lens, parallel to the lens axis, pass through the second focal point after the refraction figure 2 b. This equation is also known as the gaussian lens formula, and was discovered by edmund halley in 1693 steinhaus 1983, p. The lens makers formula is used to find the index of refraction of water in your. Thick lenses and the abcd formalism san jose state. The second focal point of a lens may be defined as the image point of an infinitely distant point object on the axis lens. The focal length of a lens depends on the refractive index of the lens and the radii of curvature.
The lens maker s equation is another formula used for lenses that. A lens is a transmissive optical device which affects the focusing of a light beam through refraction. Lenses are made from materials such as glass or plastic, and are ground and polished or molded to a desired shape. 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. Lens formula 1f 1v 1u where, f focal length of the lens, u distance of object, u distance of image. The index of refraction of the surrounding medium is n 1 if the lens is in. 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. A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction.
Thin lens formula from eric weissteins world of physics. I know the history, what the students expect from m. Cbse notes class 12 physics ray optics aglasem schools. File name enter the password open this pdf file cancel ok.
The questions and answers of how to derive lens makers formula. Lens manufacturers use the lens makers formula to manufacture lenses of the desired focal length. Derivation of lens makers formula 62582 the lens makers derivation assumes some condition, they are thin lens is used for measure the distance from surface poles to lens optical centre distance. The lens makers formula indicates that a convex lens can behave like a diverging one if m 1 m 2 i. If the answer is not available please wait for a while and a community member will probably answer this soon. Lens formula relates the image distance v, object distance u and the focal length f of the lens. 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. The derivation of lens maker formula is provided here so that aspirants can understand the concept more effectively. Derivation of lens maker formula detailed lens maker. Lens makers formula and limitations of lens makers.
Refraction by a thin lens lens with refractive index n l, made up from two intersecting spherical surfaces, surrounded by medium with n m 1 1 r 1 n n s n s n l m i l o first surface. In this video learn how to derive lens maker formula for thin lens. Curvature radius of the first surface, in meter r 2. The lens makers equation is another formula used for lenses that. The lens makers equation chapter mirrors and lenses the lens equation calculating image location calculating magnification multiple lenses ray tracing derivation lens maker formula thin lens. Hyperphysicss thick lens imaging, and a dozen subpages. The attempt at a solution i used three equations to derive the upper equation. 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.
Thick lens formula from eric weissteins world of physics. Curvature radius of the second surface, in meter this equation holds for all types of thin lenses. The lens makers formula can be derived for a concave lens in the same way. Lenses of different focal lengths are used for various optical instruments. Ci 1 p 1i 1 v 1 as the lens is thin cc 1 p 1c 1 r 1. The radial line to the point where it hits the lens surface is at an. A lens has two foci,fand, on either side of it by the sign convention. Then by the lens makers formula the ower of each half lens is given by l lleft l right r 1r 2 r. 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. Ask questions, doubts, problems and we will help you.
A concave lens is thicker at the edges and thinner in the middle. Lenses of different focal length are used for different optical instruments. The reciprocal of the focal length of a lens, when it is measured in metre, is called power of a lens. Physics notes for class 12 chapter 9 ray optics and. The surface of the lens has a radius of curvature r 1, with the centre of curvature on the opposite side of the surface to the source. Concave lens a lens which is thicker at edges and thinner at middle, is called a concave or diverging lens. A concave lens is also known as a biconcave lens because of two spherical surfaces bulging inwards. The following assumptions are taken for the derivation of lens maker formula. The radius r 2 is negative since it extends left from the second surface.
372 1094 551 970 973 28 1359 1022 1181 1548 1536 173 188 511 744 182 1079 1232 505 1247 420 1091 450 478 1145 1062 928 124 982 689 1229 853