(a) Draw a ray diagram for formation of image of a point object by a thin double convex lens having radii of curvatures R1 and R2, (a) Lens Maker’s Formula: Suppose L is a thin lens. A number of idealizations, simpliﬁcations and approximations are used to (b) Ray Diagram: The ray diagram of image formation for an object between focus (F) and pole (P) of a concave mirror is shown in fig. The refractive index of the material of lens is n2 and it is placed in a medium of refractive index n1. It is used by lens manufacturers to make the lenses of particular power from the glass of a given refractive index. The derivation of lens maker formula is provided here so that aspirants can understand the concept more effectively. If first medium is air and refractive index of material of lens be n, then 1 n 2 = n, therefore equation (v) may be written as (b) Ray Diagram: The ray diagram of image formation for an object between focus (F) and pole (P) of … The thickness of lens is t, which is very small. Lens manufacturers use the lens maker’s formula to manufacture lenses of the desired focal length. where 1n2 = n2/n1 is refractive index of second medium (i.e. An object 5 cm high is held 25 cm away from a converging lens of focal length 20 cm. Lensmaker’s Formula by C. Bond Lenses with the same shape and index of refraction will have the same focal length. Assumptions. The radii of curvature of the surfaces of the lens are R 1 and R 2 and their poles are P 1 and P 2.The thickness of lens is t, which is very small. Lens manufacturers use this relation to construct a lens of a particular power. The refractive index of the material of, axis. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students. The distance of I from pole P, This is the formula of refraction for a thin lens. Similarly a concave lens can be made convergent. Obtain lens maker’s formula and mention its significance. (a) Obtain lens makers formula using the expression. If the object O is at infinity, the image will be formed at second focus i.e. Starting with an expression for refraction at a single spherical surface, obtain Lens Maker’s Formula. If the object O is at infinity, the image will be formed at second focus i.e. A concave lens of focal length 15 cm forms an image 10 cm from the lens. Draw a ray diagram to show the formation of a real diminished image of an object by a convex lens. The ray diagram is as follows: Note: The lens maker's formula indicates that a convex lens can behave like a diverging one if m 1 > m 2 i.e., if the lens is placed in a medium whose m is greater than the m of lens. A thin convex lens having two surfaces of radii of curvature R1 and R2 is made of a material of refractive index μ2. Lens maker’s formula is the relation between the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces. The thickness of lens is t, which is very small. If first medium is air and refractive index of material of lens be n, then 1n2 = n, therefore equation (v) may be written as. SF017 SF027 51 1.5 Thin Lenses Formula and Lens maker’s Equation {Considering the ray diagram of refraction for 2 spherical surfaces as shown in figure below. What is the refractive index of the glass? The distance of I from pole P, t is negligible as compared to v', therefore from (ii), If the object O is at infinity, the image will be formed at second focus i.e. Define lens formula. O is a point object on the principal axis of the lens. Is lens formula applicable only for convex lens? O is a point object on the principal axis of the lens. (b) Define power of a lens and give its S.I. Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. The radii of curvature of the surfaces of the lens are R1 and R2 and their poles are P1 and P2. For refraction at second surface, the ray is going from second medium (refractive index n2) to first medium (refractive index n1), therefore from refraction formula at spherical surface, For a thin lens t is negligible as compared to v', therefore from (ii). The lens maker formula is a relation between the focal length, the refractive index of constituent material, and the radii of curvature of the spherical surfaces of a lens. The radii of curvature of the surfaces of the lens are R1 and R2 and their poles are P1 and P2. This formula is called Lens-Maker’s formula. The image I' acts as a virtual object for second surface and after refraction at second surface, the final image is formed at I. Draw the ray diagram and find the position, size and nature of the image formed. (a) Lens Maker’s Formula: Suppose L is a thin lens. If first medium is air and refractive index of material of lens be n, then, Obtain lens makers formula using the expression n2/v - n1/u = (n2 - n1)/R. It is defined as the reciprocal of focal length in metres. The radii of curvatures for a convex lens of a focal length 20 cm are 18 cm and 24 cm. (a) Lens Maker’s Formula: Suppose L is a thin lens. The distance of I from pole P2 of second surface is v. The distance of virtual object(I') from pole P2 is (v' -t). The refractive index of the material of lens is n2 and it is placed in a medium of refractive index n1. (b) Power of a Lens: The power of a lens is its ability to deviate the rays towards its principal axis. O C 1 II C 2 1 P 1 P 2 I2 B E A D u1 v1 v2 r1 r2 t n1 t −v1 n2 n1 SF027 52 {By using the equation of spherical refracting surface, the refraction by first surface AB and second surface DE are given by A biconvex thin lens of refractive index μ2 =1.4 has a radii of curvature R1 = 20 cm and R2 = 60 cm, μ1 = 1.5 and μ3 =1.2. Lenses of different focal lengths are used for different optical instruments. medium of lens) with respect to first medium. The distance of O from pole P1 is u. if u=. The optical centre of lens is C and X ' X is principal axis. The following assumptions are taken for the derivation of lens maker formula. The distance of O from pole P, The image I' acts as a virtual object for, surface, the final image is formed at I. If a convex lens of focal length 50cm is placed in contact coaxially with a concave lens of focal length 20cm, what is the power of the combination? The first refracting surface forms the image of O at I' at a distance v' from P1.From the refraction formula at spherical surface. If first medium is air and refractive index of material of lens be n, then 1n2 = n, therefore equation (v) may be written as. This formula is called Lens-Maker’s formula. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students. The radii of curvature of the surfaces of the lens are R, is t, which is very small. units. For refraction at second surface, the ray is going from second medium (refractive index n2 ) to first medium (refractive index n1 ), therefore from refraction formula at spherical surface, For a thin lens t is negligible as compared to v', therefore from (ii). The distance of O from pole P1 is u. The first refracting surface forms the image of O at I' at a distance v' from P1. From the refraction formula at spherical surface, The image I' acts as a virtual object for second surface and after refraction at second surface, the final image is formed at I. This formula is called Lens-Maker’s formula. The distance of I from pole P2 of second surface is v. The distance of virtual object (I') from pole P2 is (v' - t). Using this diagram, derive the magnification formula for the image formed. The focal length of a lens depends on the refractive index of the lens and the radii of curvature. (a) Obtain lens makers formula using the expression n2/v - n1/u = (n2 - n1)/R, The image I' acts as a virtual object for second surface and after refraction at second surface, the final image is formed at I.

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