Important Points in Refraction of Light at Curved Surfaces

 Refraction of Light at Curved Surfaces

• The Centre point of the sphere which contains the part of the curved surface is called the "Centre of Curvature" and it is denoted by 'C'. 
• The Geometric Centre of the curved surface is called the Optical Centre and it is denoted with 'P'.
• The line drawn from the Centre of Curvature to the pole or any point on the curved surface is called the Radius of Curvature and it is denoted with 'R'.  Radius of Curvature itself is the normal line at that point on the curved surface.
• The line passes from the Centre of Curvature and the Pole is called the Principal Axis.
• A ray which passes through rarer medium and incident on a surface separating rarer medium and denser medium, after entering into denser medium it bends towards the normal line, the bending of the light ray is called Refraction of Light.  The light ray after refraction is called Refracted ray and the angle after refraction is called Angle of Refraction.
• As per Snell's Law the rays which move along the normal to the surface do not deviate.
• The parallel light ray to the principal axis after refraction intersects the principal axis at a point, this point is called Focal Point or Focus.
• The point of convergence or point from which rays seem to emanate is called Focal Point or Focus. Every lens has two focal points.
• The ray passing through the focal point will take a path parallel to the principal axis after refraction.
• The distance between Focus and Pole is called Focal Length.
• The light rays which move very close to the principal axis are called Paraxial Rays.
• The ratio between velocity of light in vacuum to the velocity of light in medium is called the Refractive Index. Refractive Index is n=c/v.
• The relation between refractive indices of media, object distance, image distance and radius of curvature is  n2/v-n1/u=n2-n1/R. For the plane surfaces n2/v=n1/u.
•  Lens is formed when a transparent medium has two surfaces of which one or both curved.
• If a lens has two curved surfaces bulging outward is called a double or bi Convex Lens.
• If a lens has two curved surfaces curved inward it is called a double or bi Concave Lens.

• The ray which passes along the principal axis and through the Optical Centre is un deviated.
• When parallel rays fall on a lens with a certain angle with principal axis, after refraction the rays converge at a point on the focal plane or appear to diverge from a point on the focal plane.
• A perpendicular line to the principal axis drawn at focus is called Focal Plane.
• Sign Conventions for lens 1) All distances are measured from the Optical Centre. 2) Distance measured in the direction of the incident light ray is taken as positive 3) Distance measured opposite to the incident ray is taken as negative. 4) The heights measured above the principal axis are taken as positive. 5) The heights measured below the principal axis are taken as negative.
• Lens Formula is 1/f=1/v-1/u.
• The focal length of the lens depends on the surrounding medium in which it is kept.
• Lens makers formula 1/f=(n-1)[1/R1-1/R2].
• The concave lens mostly converges light rays that's why it is called a converging lens.
• The convex lens always diverges the light rays that's why it is called a diverging lens.
• The convex lens behaves as a converging lens, if it is kept in a medium with less refractive index than the refractive index of the lens.
• The convex lens behaves like a diverging lens when it is kept in medium with greater refractive index than the lens. 
• The bubble of soap water behaves like a diverging lens.
• Two draw ray diagrams for lenses we need to use light rays one parallel to the principal axis, second ray passing through optical centre, third ray passing through focus and last the ray passing through centre of curvature.  From given rays any two are used to draw the ray diagrams.
• If the object is at infinite distance before a Concave lens, the image is formed on focus.  The image is point size.
• If the object is placed beyond the Centre of Curvature before a concave lens, the image is formed between the F & C opposite side of the lens. The image is real, smaller in size and inverted.
• If the object is placed on the Centre of Curvature before a concave lens, the image is also formed on C, and the image is same in size, real and inverted.
• If the object is placed between Focus and Centre of Curvature before a concave lens, the image is formed beyond Centre of Curvature. The image is real, enlarged and inverted.
• If the object is placed on Focus before a concave lens, the image is formed at an infinite distance. 
• If the object is placed between Optical Centre and Focus before a concave lens, the image is formed on the same side.  The image is erect, enlarged and virtual.
• If an object is placed at any point before a convex lens, the image always forms between Optical Centre and Focus.  The image is erect, virtual, and smaller than the object.
• The image which can be caught on the screen is called a Real image.
• The image which can not be caught on the screen is called a Virtual image.