Everyone wants to explain but not many have the talent, but i have it. Lens makers formula example consider a convex lens or concave lens of absolute refractive index. 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. 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. 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. Lens makers formula definition, examples, diagrams. 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 makers formula is used to find the index of refraction of water in your. Since the angle between two tangents forming a prism is equal to the angle between two radii, so we have. I know the history, what the students expect from m. Cbse notes class 12 physics ray optics aglasem schools. In this video learn how to derive lens maker formula for thin lens. A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. 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. Hyperphysicss thick lens imaging, and a dozen subpages.
The questions and answers of how to derive lens makers formula. Thin lens formula from eric weissteins world of physics. 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 can be derived for a concave lens in the same way. The lens makers equation is another formula used for lenses that. A point source lies on the optical axis of the lens, a distance u away from the centre of the lens. Real surfaces reflective derive power of mirror by placing object at center of curvature. Lens formula relates the image distance v, object distance u and the focal length f 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 lens maker formula is commonly used by lens manufacturers for manufacturing lenses of desired focal length. These equations, called the thinlens equation and the lens makers equation, allow us to quantitatively analyze thin lenses. 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. Then by the lens makers formula the ower of each half lens is given by l lleft l right r 1r 2 r. Physics notes for class 12 chapter 9 ray optics and.
Consider the thick biconvex lens shown in figure \\pageindex8\. 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 focal length of a lens depends on the refractive index of the lens and the radii of curvature. Lens makers formula is the relation between the focal length of a lens to the refractive index of its material and the radii of. Lenses of different focal lengths are used for various optical instruments. 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. The focal length of a lens depends upon the refractive. Derivation of lens maker formula detailed lens maker.
The derivation of lens maker formula is provided here so that aspirants can understand the concept more effectively. A lens maker formula may be defined as the formula which gives the. Lens manufacturers use the lens makers formula to manufacture lenses of the desired focal length. Lenses are made from materials such as glass or plastic, and are ground and polished or molded to a desired shape. 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. 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. The lens maker s equation is another formula used for lenses that. For a double convex lens the radius r 1 is positive since it is measured from the front surface and extends right to the center of curvature. 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. File name enter the password open this pdf file cancel ok. The following assumptions are taken for the derivation of lens maker formula. Since ray strikes surface normally, it must return to the same point. A beam of light from the source moves towards the lens at an angle.
The equation relating the object distance u, the image distance v and the focal length f of the lens is called the lens formula. 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. Some people thought that magnification was the sole contributor to resolution. 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.
Numerical methods in lens a lens formula definition. A lens is a transmissive optical device which affects the focusing of a light beam through refraction. If the answer is not available please wait for a while and a community member will probably answer this soon. Remember that by our sign convention, r derivation of lens maker formula is provided here so that aspirants can understand the concept more effectively. Ci 1 p 1i 1 v 1 as the lens is thin cc 1 p 1c 1 r 1. If a lens is thicker than that measure, the thin lens equation cannot be used. This derivation is not fundamental, but it is more intuitive. 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. Thick lens formula from eric weissteins world of physics. A concave lens is also known as a biconcave lens because of two spherical surfaces bulging inwards. 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. A lens has two foci,fand, on either side of it by the sign convention. 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 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.
Let c 1 and c 2 be the centre of curvature of the two spherical surfaces. Please note the following so you can understand how the thin len equation can be derived. The attempt at a solution i used three equations to derive the upper equation. The refracted ray from a suffers a second refraction on the surface xp 2y and emerges along bi. Lenses of different focal length are used for different optical instruments. It follows from the refraction due to convex spherical surface xp 1y. O c 1 ii c 2 1 p 1 p 2 i2 b e a d u1 v1 v2 r1 r2 t n1 t. Concave lens a lens which is thicker at edges and thinner at middle, is called a concave or diverging lens. A concave lens is thicker at the edges and thinner in the middle. Thick lenses and the abcd formalism san jose state. 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. 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. Ask questions, doubts, problems and we will help you. The radial line to the point where it hits the lens surface is at an.
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