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. Using the positive optical sign convention, the lens makers formula states where f is the focal length, n is the index of refraction, and and are the radii of curvature of the two sides of the lens. 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. Lens maker s formula using the positive optical sign convention, the lens maker s formula states where f is the focal length, n is the index of refraction, and and are the radii of curvature of the two sides of the lens. You calculate how it changes on the first boundary that s some insight that says that one creates some image of the original object and the redirected photons seem to come from the image. Now we would like to reinterpret the meaning of the usual lens formula. Lens makers formula definition, examples, diagrams toppr. Fermats principle to derive lens formula physics forums. Lens makers formula is the relation between the focal length of a lens to the refractive index of its material and the radii of. The radii of curvature here are measured according to the cartesian sign convention. 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. Due to the geometrical symmetry, the thin lens equation can be used for a convex and concave mirrors.
Using the formula for refraction at a single spherical surface we can say that, for the first surface, for the second surface, now adding equation 1 and 2, when u. The formula for surface power is ds u1r, where u is the index of refraction and r the radius of curvature in meters. Ci 1 p 1 i 1 v 1 as the lens is thin cc 1 p 1 c 1 r 1. 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. Point e is the center of curvature of the right surface of the lens and ed is normal to the surface. The complete derivation of lens maker formula is described below. Heres a picture of light going through a lens index of refraction of 1. 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. For a double convex lens the radius r 1 is positive since it is measured. Otherwise, replace n with the ratio of the refractive indices.
For the past 1 hour, im trying to derive lens maker s equation using fermat s principle, which of course is our homework. Curvature radius of the second surface, in meter this equation holds for all types of thin lenses. A thin lens is defined as a lens with a thickness that is approximately ignorable compared with the radii of curvature of the lens. The word lens comes from lens, the latin name of the lentil, because a doubleconvex lens is lentilshaped. For the past 1 hour, im trying to derive lens makers equation using fermats principle, which of course is our homework. Onsider a lens having index of refraction n2 and s. As b and d both are close to the optical centre of the lens, bo. 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. Oct 07, 2014 here s a picture of light going through a lens index of refraction of 1. Lens manufacturers use the lens maker s formula to manufacture lenses of the desired focal length. Derivation of lens maker formula detailed lens maker.
Check the limitations of the lens makers formula to understand the lens maker formula derivation is a. How does the lens formula follow from fermats principle. Lenses of different focal length are used for different optical instruments. The refracted ray from a suffers a second refraction on the surface xp 2y and emerges along bi. We can now combine 5 and 6 noting that the image of the first lens is a. For a thin lens, the power is approximately the sum of the surface powers. Notice that 1q is the final curvature cf, of the wave front after the wave front has passed the lens. The baby chef flawless formula maker is the goofproof solution for all parents who feed their babies powdered formula. The bottom path goes in a straight line, so its the shortest. This relation always gives a negative focal length f as expected for a double concave lens because it is a diverging lens.
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. 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. This formula maker takes the guesswork out of mixing dry formula into a smooth liquid for easy, messfree formula preparation. The focal length of a lens depends on the refractive index of the lens and the radii of curvature. Lens makers formula and limitations of lens makers formula. Ciconverging lens di tdivergent lens lens makers equation note that this assumes that the lens is placed in air. A beam of light from the source moves towards the lens at an angle. Lens makers formula from eric weissteins world of physics. Lens power in diopters m1 is equal to 1f, where f is the focal length expressed in meters. If a lens is thicker than that measure, the thin lens equation cannot be used. Applying the equation of paraxial refraction with air to each surface gives. Image formed due to reflection on a spherical surface.
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. The radius r 2 is negative since it extends left from the second. Thick lens formula from eric weissteins world of physics. It follows from the refraction due to convex spherical surface xp 1y. 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.
A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. Derive a generalized lens makers equation to replace the equation 1fn. Lens maker s 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. Experimental determination of focal length of lenses result. Ci 1 p 1i 1 v 1 as the lens is thin cc 1 p 1c 1 r 1. Lens manufacturers use the lens makers formula to manufacture lenses of the desired focal length. Question about lens makers formula physics stack exchange. Now using this i have to derive lens makers formula. 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. Feb 02, 2007 homework statement a plane convex lens is made of glass index 1. If fermats principle says that light takes the fastest path, which path is that. 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. Isaac physics a project designed to offer support and activities in physics problem solving to teachers and students from gcse y11, through to university.
A lens maker formula may be defined as the formula which gives the. 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. You calculate how it changes on the first boundary thats some insight that says that one creates some image of the original object and the redirected photons seem to come from the image. Curvature radius of the first surface, in meter r 2. The radial line to the point where it hits the lens surface is at an. 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. 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 double concave lens see figure below, the lens makers formula has a slightly different form. The lens makers equation is another formula used for lenses that.
If you want me to teach you biology or chemistry or physics. A lens has two foci, f and, on either side of it by the sign convention. Picture the problem we can use the lens makers equation to find the focal length of each of the lenses described in the problem statement. Lens makers formula and limitations of lens makers. If fermat s principle says that light takes the fastest path, which path is that. The focal length of a lens depends upon the refractive. You can change the curvature of the surface of the material as well as the index of refraction.
Homework statement a plane convex lens is made of glass index 1. This equation is used for determining the focal length of a thin lens thickness 0 with radii of curvature r1 and r2. In this video learn how to derive lens maker formula for thin lens. For a double concave lens see figure below, the lens maker s formula has a slightly different form. The advanced technology and magnetic whisk create lumpfree, nonaerated results every time.
1132 848 614 297 37 137 1489 1067 202 424 682 1497 771 1123 566 838 1 931 1255 1280 886 20 836 1302 247 730 573 313 257 809 446 612