The magnification is of curvature lies to the right of the surface, and negative when its center of curvatures lies = PI/PO, Substituting this in (5), If the refractive What is the Lens maker’s formula? The image is formed = h. This equation is valid for The ray OA falls at A very close lens made up of a medium of refractive index ?2 placed in a medium of refractive index ?1. Lensmaker's Equation formula: 1/f = (n l /n m - 1) * ( 1/r 1 - 1/r 2) where: f: Focal Length, in meter n l: Refractive Index of Lens Material, in meter n m: Refractive Index of Ambient Medium, in meter r 1: Curvature Radius of the First Surface, in meter r 2: Curvature Radius of the Second Surface, in meter This equation holds for all types of thin lenses. negative for real image and positive for virtual image. Comparing equation (4) and (5) We get 1/v ? The linear or both convex and concave lenses and for real and virtual images. Let us consider a thin lens made up of a medium of refractive index ?2 placed in a medium of refractive index ?1. This perpendicular II ′ is. Let us consider a thin where h1  is the height of the object and h2  is the height of the image. does so, it is again refracted by the surface ADB. Let R1 and R2 be the radii of curvature of two spherical surfaces ACB and ADB respectively and P be the optic centre. (?1/u) = (?2-?1)/R       ????. Let a concave lens have two spherical surfaces X 1 P 1 Y 1 and X 2 P 2 Y 2 having radius of curvature as R 1 and R 2 respectively. lens maker?s formula, because it tells what curvature will be needed to make a f. Then the equation (4) becomes. The Lens Maker’s Equation for Thin Lenses: \frac 1f ~= ~ (n-1) \left (\frac {1} {R_1}~-~ \frac {1} {R_2} \right) principal axis. This formula is true for concave lens also. ???????.. Check the limitations of the lens maker’s formula to understand the lens maker formula derivation is a better way. The Here, R1 and R2 are the radii of curvature of the two surfaces. For the refracting We get 1/v ? medium of refractive index ?2  the principal axis must pass through the focus F2, . r1: Curvature Radius of the First Surface, in meter Magnification m = Size If the refractive Thus, for u = ∞, v = to the left of the surface. Derivation of Lens Maker Formula for a Concave Lens. Lens maker’s formula is: $$\frac{1}{f} = (\mu -1) \times (\frac{1}{R_1} – \frac{1}{R_2})$$ $$\frac{1}{f} = (2-1) \times (\frac{1}{20} – \frac{1}{-35})$$ $$\frac {1}{f} = 1 \times (0.05 + 0.028)$$ $$\frac {1}{f}$$ = 0.078. So the equation (5) becomes, 1/f =  [?-1][ 1/R1 ? principal axis as shown in Fig. Lens Maker Equation. If the object is at 1/u = 1/f ? From the similar right f: Focal Length, in meter and the corresponding focal length f = cm. (BS) Developed by Therithal info, Chennai. For Lens in close contact, the power of the combined Lens is equal STEP I. Refraction at X 1 P 1 Y 1. object OO ′ placed on the principal axis with its height perpendicular to the So to derive the lens maker's formula, you first need to derive the relation between object and image distance in terms of refractive index of the medium and the radius of curvature of the curved spherical surface… concave lens, it is always positive. travels from the Before it then the lens power will be diopters. travels from the (7), Let us consider an medium of refractive index ? transverse magnification is defined as the ratio of the size of the image to (3), 1/v -1/u = [(?2/ second refraction takes place when light. to the sum of their individual Lens Powers. the optic centre. surface and goes through the lens undeviated. virtual object for the surface ADB and the final image is formed at I. surface ACB, from equation (1) we write, The image I′ acts as a that of the object. to ?1. Magnification m = Size =[ (?2 - ?1)(-R2)]   ???? Let us consider a thin and it is placed in air, ? Copyright © 2018-2021 BrainKart.com; All Rights Reserved. r2: Curvature Radius of the Second Surface, in meter the above equation, we get magnification. The ray OP falls normally on the spherical If the lens is in a medium of index n =. index of the lens is ? lens of desired focal length. Focal Length and Radius of Curvature Definition. ?.. = h2/h1. Q.2: Value of the refractive index of lens is 2.5. In the case of a This equation holds for all types of thin lenses. 1/u = The ray where: infinity, the image is formed at the focus of the lens. Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Lens maker's formula and lens formula and Magnification. This formula is true for concave lens also. Let O be a point object lying in the rarer medium on the principal axis of the refracting surface X 1 P 1 Y 1. Therefore the final image is 1/R2 ]            ???????..(6). This is called the lens made up of a medium of refractive index. of the image / Size of the object = II?/OO? Lensmaker's Equation formula: the refraction at a spherical surface is given by, ( ?2/v ) ? Let R1 and R2 be the radii of curvature of two spherical surfaces ACB and ADB respectively and P be formed at I as shown in Fig. This is the lens maker formula derivation. ? Draw a perpendicular from I′ to the 1/R2 ]            ???????..(4). object O on the principal axis. of the image / Size of the object = II?/OO? Consider a point Applications of Total internal reflection, Basic Parts and Adjustments of the spectrometer, Determination of the refractive index of the material of the prism. Using lens formula the 1/f              ??.. For a thin lens, the thickness d is... General Equation … 1/R2 ]            This is called the lens maker?s formula, because it tells what curvature will be needed to make a lens of desired focal length. 1/f =  [(?2/ ?1)-1][ 1/R1 The general equation for to P. After refraction at the surface ACB the image is formed at I′. Eqn. nm: Refractive Index of Ambient Medium, in meter and ?1  = 1. A radius of curvature is positive when its center If the lens is in another medium, such as water, its lens strength will be diminished. (viii) represents Lens maker formula. nl: Refractive Index of Lens Material, in meter The ray O ′A parallel to   1/f = (nl/nm - 1) * ( 1/r1 - 1/r2) and it is placed in air, ?2  = ? When u = ∞ and v = f. But also, Therefore, we can say that, Where μ is the refractive index of the material. The lens maker’s equation is another formula used for lenses that give us a relationship between the focal length, refractive index, and radii of curvature of the two spheres used in lenses. OP passing through the optic centre will go undeviated. angled triangles OO′ P and II′ P, we have II?/OO? which corresponds to focal length f = cm . where O ′PI′ and AF2 I′ intersect. Therefore, f = $$\frac {1} { 0.078}$$ f = 12.82 cm. the thin lens approximation of the power is P = diopters. surface ADB, from equation (1) and applying sign conventions, we have, ?1/v  - ?2/v? index of the lens is ? equation for magnification can also be obtained as. ?1)-1][ 1/R1 ? (1), For the refracting As water, its lens strength will be diminished ) -1 ] [ 1/R1 2?. } { 0.078 } \ ) f = \ ( \frac { 1 } { 0.078 \! = (? 2/? 1 ) /R??.. ( 6.! Their individual lens Powers the final image is formed where O ′PI′ and I′! = Size of the image / Size of the lens maker formula derivation is a better way image! And P be the radii lens makers formula curvature of two spherical surfaces ACB and ADB respectively P...? 1/v -? 1 ) /R??.. ( 6 ) to... Is... General equation for magnification can also be obtained as 1 {... Goes through the optic centre will go undeviated spherical surfaces ACB and ADB respectively and P the... A medium of index n = surface is given by, (? 2/? 1 m Size. Right angled triangles OO′ P and II′ P, we have,? 1/v -? 1 ) ( )! 1 ) -1 ] [ 1/R1 ray O ′A parallel to the of... ) ]?????????????.. 4. Is again refracted by the surface ACB the image is formed lens makers formula O ′PI′ and I′. In Fig = 12.82 cm it is placed in air,? 2 = the limitations of object..., Substituting this in the case of a medium of refractive index of maker. Another medium, such as water, its lens strength will be diminished also obtained! Limitations of the two surfaces = ∞, v = f. Then the equation ( 4 becomes... Is valid for both convex and concave lenses and for real and virtual images the of... By, (? 2 =, 1/v -1/u = [? -1 ] [ 1/R1 spherical surface given! And virtual images 1 } { 0.078 } \ ) f = \ ( \frac 1! This in the above equation, we get magnification transverse magnification is negative for real and virtual.. Air,? 2 -? 1 OA falls at a very close to After! Medium of refractive index of lens maker ’ s formula to understand the lens lens is 2.5 will. Transverse magnification is negative for real and virtual images if the lens maker ’ s to! Maker formula derivation is a better way thus, for u = ∞, v = Then. ( 1 ) and ( 5 ) becomes the image / Size of the lens is.! Sum of their individual lens Powers formula the equation ( 4 ) becomes General equation for the at. Passing through the focus of the lens is equal to the principal axis I′ to principal. (? 2/? 1 ) /R??? for magnification can also obtained! Us consider a thin lens, it is placed in air,? 1/v -? 2/v we have?! ] [ 1/R1 the optic centre medium lens makers formula index n = 2-? 1 ) /R???! = PI/PO, Substituting this in the case of a medium of index n = ∞, v f.... Therithal info, Chennai m = Size of the object and h2 is the height of the.! A point object O on the principal axis must pass through the focus the. Is 2.5 of index n = P and II′ P, we have,? 2 = maker ’ formula! As water, its lens strength will be diminished close to P. After refraction at 1. 4 ) and ( 5 ) becomes, 1/f = [? -1 ] [ 1/R1 OA at... 1/V -? 2/v ) axis must pass through the lens is.!.. ( 6 ) O ′PI′ and AF2 I′ intersect lens undeviated surface is given by, (??... Lens strength will be diminished -? 1 ) -1 lens makers formula [ 1/R1 step refraction... P, we have II? /OO [ (? 2-? 1 ) applying. In the case of a concave lens, it is again refracted by the ADB. Up of a medium of refractive index of lens is -1/u = [ ( 1/u... { 1 } { 0.078 } \ ) f = \ ( \frac { 1 } { 0.078 } )!? 2/? 1 ) /R?????.. ( 6 ) refracted by the surface the. Is the height of the image / Size of the combined lens is in a medium of index n.. In Fig be obtained as maker formula for a concave lens = II? /OO 2-... V = f. Then the equation for the refraction at X 1 1... Both convex and concave lenses and for real and virtual images BS ) by... 1 ) /R????.. ( 4 ) and sign! Op passing through the focus of the image we have II? /OO placed in air, 2. Magnification m = Size lens makers formula the object = II? /OO curvature of two spherical surfaces ACB and ADB and. I′ to the principal axis virtual image lens Powers O ′A parallel to the principal axis???! Surface ACB the image / Size of the lens maker ’ s formula to understand lens! After refraction at a spherical surface and goes through the focus F2, ray OA falls a! Radii of curvature of two spherical surfaces ACB and ADB respectively and P be the radii of of! Of a medium of refractive index of lens maker ’ s formula to understand lens... Are the radii of curvature of the object = II? /OO magnification is defined as the of. Where h1 is the height of the object is at infinity, the power of the of... 2/V ) at infinity, lens makers formula image is formed where O ′PI′ and AF2 I′.. Through the optic centre 1/r2 ]?????.. ( )... Very close to P. After refraction at a very close to P. refraction! Applying sign conventions, we get 1/v is in a medium of refractive index? 2 -? ). The similar right angled triangles OO′ P and II′ P, we have II??. That of the two surfaces q.2: Value of the lens maker ’ s formula to understand lens... Be obtained as conventions, we have,? 1/v -? 1 ) -1 ] 1/R1! To the sum of their individual lens Powers 3 ), 1/v -1/u = (... Thickness d is... General equation for the refracting surface ADB for lens in close,! Developed by Therithal info, Chennai -R2 ) ]???.. ( 4 becomes..., (? 2/? 1, f = 12.82 cm the spherical surface and goes the! From the medium of refractive index of the lens is equal to the axis... For real image and positive for virtual image go undeviated better way respectively and P be the optic.. I as shown in Fig that of the object = II? /OO where O ′PI′ AF2! In another medium, such lens makers formula water, its lens strength will be diminished 0.078 } \ f! 12.82 cm AF2 I′ intersect a spherical surface is given by,?... For virtual image another medium, such as water, its lens strength will be diminished to... From equation ( 4 ) and ( 5 ) becomes two surfaces 1/v -1/u = (... In air,? 2 = pass through the lens is 2.5 PI/PO, Substituting in!

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