{\displaystyle K} ) {\displaystyle R} {\displaystyle r=0} Sign conventions 4 • Light travels from left to right • A radius of curvature is positive if the surface is convex towards the left • Longitudinal distances are positive if pointing to the right • Lateral distances are positive if pointing up • Ray angles are positive if the ray direction is obtained by rotating the {\displaystyle K} This means that they have been given a curvature 1/f. If A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. a convex lens describe the deviation of the surface from the axially symmetric quadric surface specified by This means that the outer portions move off more rapidly first and so the curvature of the wave is further increased so converging the light more strongly. This means that the outer portions of the wave ‘catch up’ so increasing the curvature to form a converging beam. Radius of curvature (ROC) has specific meaning and sign convention in optical design. 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. diverges the waves. ). r In the example below they are bent from a plane wave to form a converging wave in the lens. You can follow this change of curvature as the waves meet the lens and then pass through it, emerging at the other side. Radius of curvature (ROC) has specific meaning and sign convention in optical design. The radius of curvature of a convex mirror used for rearview on a car is 4.00 m. If the location of the bus is 6 meters from this mirror, find the position of the image formed. Wavefronts Wavefronts spreading outwards from a point source are taken as having a negative curvature and so the distance from the lens to the object is negative Wavefronts that converge to an image are taken as having a positive curvature and so the distance from the lens to the image is positive. α K The lens adds a constant curvature (1/f) to the wave and so the equation relating the object distance (u) image distance (v) and the focal length (f) is: using the above sign convention called the Cartesian sign convention This can be shown in the following diagram. from the axis. 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 {\displaystyle \alpha _{1}} and These surfaces are typically designed such that their profile is described by the equation, where the optic axis is presumed to lie in the z direction, and i D @ñÿ D N o r m a l $CJ OJ QJ ^J _HaJ mH sH tH @ @ @ H e a d i n g 1$@&. Note however that in areas of optics other than design, other sign conventions are sometimes used. 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 Then pass through it, emerging at the other side //en.wikipedia.org/w/index.php? title=Radius_of_curvature_ ( optics ) & oldid=980175178 Creative. 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