# sign convention for radius of curvature of lens

and ( This page was last edited on 25 September 2020, at 01:36. Looking at the diagram you can see that waves with no curvature have been converged to a point a distance f (the focal length) from the lens. describe the deviation of the surface from the axially symmetric quadric surface specified by A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. {\displaystyle r=0} (Remember that 1/f will be positive for a convex lens and negative for a concave lens) The example has been done with a plane wave but the same would occur with a spherical wave spreading outwards from a point object. A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. {\displaystyle R} For the general mathematical concept, see, https://en.wikipedia.org/w/index.php?title=Radius_of_curvature_(optics)&oldid=980175178, Creative Commons Attribution-ShareAlike License. PAGE PAGE 2 N e g a t i v e d i s t a n c e s ( f o r o b j e c t s o n t h e l e f t o f t h e l e n s ) P o s i t i v e d i s t a n c e s ( f o r i m a g e s o n t h e r i g h t o f t h e l e n s ) P o s i t i v e d i s t a n c e s - + " F i g u r e 1 F o c u s W a v e l e n g t h i n a i r lğ W a v e l e n g t h i n g l a s s lğ W a v e l e n g t h i n a i r lğ " - - - + + + m e n i s c u s b i - c o n c a v e b i - c o n v e x p l a n o - c o n c a v e p l a n o - c o n v e x E x a m p l e 1 / v = 1 / u + 1 / f F o r a l e n s o f f o c a l l e n g t h + 2 0 c m ( c o n v e x ) , o b j e c t d i s t a n c e 5 0 c m ( o n l e f t o f t h e l e n s ) 1 / v = 1 / 2 0 1 / 50 = 0.03 Therefore: v = 33.3 cm (positive so on the right hand side of the lens) u v O I Curvature of waves leaving the lens = curvature of waves hitting the lens + curvature added by the lens Lens equation: 1/v = 1/u + 1/f Figure 2 Figure 3 Figure 4 Figure 5 V W I J O P ` q c d x y À Á ñ ò ø ù ú ü ı The distance from the vertex to the center of curvature is the radius of curvature of the surface.[1][2]. Waves and curved surfaces When light waves fall on a curved surface that surface changes the curvature of the wave. R 2 is the radius of curvature and = Note however that in areas of optics other than design, other sign conventions are sometimes used. and The vertex of the lens surface is located on the local optical axis. For thin lenses we can use the lens maker's equation: 1 f = ( n − 1) ( 1 R 1 − 1 R 2) Where n is the index of refraction of the material, R 1 is the radius of curvature of the side the light hits first, and R 2 is the radius of curvature of the side the light hits last. from the axis. K A surface that converges a wavefront is taken a positive e.g. In particular, many undergraduate physics textbooks use the Gaussian sign convention in which convex surfaces of lenses are always positive. As the wave hits the lens it is the centre of the wave that meets the glass first and so this part of the wave is slowed down first (light waves move slower in glass than they do in air). a convex lens a b ğ ñ H I Ì Í Î Ù p ú û w x z ¿ À í î ï ğ ñ ı ı ı ı ı ı ø ø ø ø ø ı ı ö ø ø ı ô ò ı ı ı ı ı ı ı ı ı $a$ ñ ú û ü F ” – ¤ Ê * , ’ ” ˜ š � ¤ ¦ ¸ º ö ğ î ö ğ î î î î ì ì î ì ì ì ì ì î î î î î î î ç î $a$ „h]„h „øÿ„ &`#$ º Æ È ò ô $ & P R V X \ ^ b d h j n p t v z | � � ¦ ¨ ¼ ¾ ú ø ú ø ú ø ú ø ø ø ø ø ø ø ø ø ø ø ø ø ø ø ú ø ú ø ú ø $a$ ¦ ¨ ¼ ¾ Ú Ü ö ø S U W X Z [ ] ^ ` a É Ë ñ ó ü ı ı ı ı ı û û ÷ í ÷ ê ı ı ı ı CJ 5�OJ QJ \�^J 5�\� 5�CJ ¾ Ú Ü ö ø

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