Thin lens formula derivation pdf merge

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. Purpose to observe the operation of thin lenses and gain experience with the placement and alignment of optical components. According to lens makers formula, where, f is the focal length of the lens, u is the object distance, and v is the image distance. O c 1 ii c 2 1 p 1 p 2 i2 b e a d u1 v1 v2 r1 r2 t n1 t.

For a given aperture and focal length, the amount of spherical aberration in a simple lens is a function of object position and the shape, or bending, of the lens. To derive the thin lens equation, we consider the image formed by the first refracting surface i. 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. 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. Thin lens formula for concave and convex lenses byjus. Propagation of errorsbasic rules university of washington. The goal is to measure the radius of curvature and focal length of a single converging lens from which you can calculate the index of refraction n. Using the newtons lens formula one can calculate the focal length of the two lens system. The simplest example here is of two thin lenses with a spacing l between them, for which we can derive. A statement of the approximation involves the optical axis, which is a line that passes through the center of each lens and is oriented in a direction normal to the surface of the lens at the center.

In figure 1, let the be focal lengths of the two lenses be f 1 and f 2. If the thickness of a lens is negligible in comparison to the radius of curvature, it is a thin lens. In this video i will explain the lensmakers equation apply to a thick lens in air. For the love of physics walter lewin may 16, 2011 duration. To examine and measure real and virtual images in simple optical systems. In each case, we derive the lens equation it always turns out to be the same equation, by drawing the ray tracing diagram and analyzing the similar triangles that appear in it.

Imaging with two lenses graphical methods parallelray method, find intermediate image, use as. As a simple case, consider a pair of thin lenses in air. Image servers as a virtual object for the second lens. Lens makers formula and combination of thin lenses found mistakes report here. In many optical instruments there may be compound lenses, that is, two or more lenses in contact. The thin lens equation is also sometimes expressed in the newtonian form. Numerical methods in lens a lens formula definition. If a lens is thicker than that measure, the thin lens equation cannot be used. Apply imaging formula to first lens to find image in that lens. The distance from this point to the first deflection from parallel is the focal length, usually expressed as ve for a divergence. The following assumptions are taken for the derivation of lens maker formula.

We can rewrite the lensmakers formula in a form of. The thin lens approximation is good as long as \i\, \o\, and \f\ are all large compared to the thickness of the lens. For a thin lens, the lens power p is the sum of the surface powers. The distance for the lens or lens set to converge an incoming parallel beam to a single point. This paper describes how to properly use the thin lens formula to model a 35mm camera thick lens, even at minimum focus distances and how to accurately measure and determine the location of all cardinal points in the model for a real 35mm lens.

Due to the geometrical symmetry, the thin lens equation can be used for a convex and concave mirrors. The second ray is towards the optical center such that it passes undeviated. We shall explicitly consider the errors that accompany. A thin lens is defined as a lens with a thickness that is approximately ignorable compared with the radii of curvature of the lens. How to use the thin lens formula to model a thick lens.

This discussion on how to derive lens makers formula. This is known as thin film interference, because it is the interference of light waves reflecting off the top surface of a film with the waves reflecting from the bottom surface. The overall idea of how were going to approach is this. The equation relating the object distance u, the image distance v and the focal length f of the lens is called the lens formula. A two lens system is studied using the newtons lens equation. Our first step is to determine the conditions for which a lens will produce an image, be it real or virtual.

The thin lens equations are broadly applicable to all situations involving thin lenses and thin mirrors. The following typical equation is used to determine a relation between the focal length of the lens, the distance of object and distance of. Thin lens equation add these equations and simplify using 1 and 0. After watching this lesson, you will be able to explain what a lens is both concave and convex, list uses of lenses in everyday life, and use the thin lens equation to solve problems. Thin converging lens this experiment is a classic exercise in geometric optics. Let us consider the thin lens shown in the image above with 2 refracting surfaces having the radii of curvatures r1 and r2 respectively. Figure a figure b figure c the above figure shows the image formation by a convex lens.

Consider a convex lens with object ab kept on the principal axis. Study of twolens system with the method of newtons lens. Oa object distance uoa1 image distance vof2 focal length fc c 16. According to this, the equation of thin lens may vary. For an image to be produced, all rays at the image plane which come from one particular point on the object must pass through one corresponding particular point in the image plane.

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. For thicker lenses, gullstrands equation can be used to get the equivalent power. The derivation of the gaussian form proceeds from triangle geometry. January 03 lasers 51 example, two separated positive lenses. The equation derived for a thin lens and relating two conjugated points is. If we neglect small distance between the lenses,the distance of this virtual object from lens l 2 will be the same as its distance from l 1. For a diverging lens or set extend the diverging rays backwards until they converge on the optic axis. By identifying two sets of similar triangles, we will be able to derive the thin lens equation. Lensmakers equation for thick lens in two different media. The questions and answers of how to derive lens makers formula. We will now present a simple way of calculating or proving this formula using raytracing.

Derivation of lens formula convex lens let ab represent an object placed at right angles to the principalaxis at a distance greater than the focal length f of the convex lens. Derivation of lens maker formula detailed lens maker. Science class 12 physics india ray optics and optical instruments refraction in thin lenses. Shows how to use the thin lens equation to calculate the image distance, image height and image orientation for convex lenses when the object distance is greater the the focal length f. We take the limit of \t0\ to obtain the formula for a thin lens. Thin lenses and optical instruments university of calgary. Physics equationsparaxial approximation wikiversity.

Refraction at spherical surfaces in paraxial approximation 2. Thick lenses and the abcd formalism san jose state. We may apply the thin lens equation and cascade the imaging process by taking the image formed by lens 1 as the object for lens 2. Interference between light waves is the reason that thin films, such as soap bubbles, show colorful patterns. Thin lens formula with magnification for concave and convex lenses. We will first deal with the case of two thin lenses in contact. An extended hemispherical lens is a special type of planoconvex lens, in which the lens s curved surface is a full hemisphere and the lens is much thicker than the radius of curvature.

The thin lens equation and the magnification equation example. The image a1b1 is formed beyond 2f2 and is real and inverted. The paraxial approximation can be used to derive simple equations involving lenses. Then the 2nd lens is going to create an image of that image and so what were basically going to do is were going to use the thin lens formula. The is the power of lens which is measured in diopters. 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 paraxial approximation approximation is valid for rays that make a small angle to the optical axis of the. The distance from the first lens to the primary principal point is etf2f. The virtual image formed by a diverging lens an object is placed 7. For latest information, free computer courses and high impact notes visit. Lens formula derivation with simple steps and diagram byjus. 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. This 1st lens is going to create an image of this object over here. Their distance d has been varied and four positions have been used during the experiment.

Notes, exercises, videos, tests and things to remember on lens makers formula and combination of thin lenses. Lens makers formula and combination of thin lenses. Two rays are considered such that one ray is parallel to the principal axis and after reflection, it passes through the focus. If l 2 forms an image i 2 of this virtual object at a distance q 2 then p 2. On this slide, you see a schematic of a principal ray diagram.