Reflection and Refraction of Light

• The chapter focuses on reflection and refraction of light, using the straight-line propagation model
• It covers reflection by spherical mirrors and refraction, along with real-world applications

Reflection of Light

• Reflection: the phenomenon where a highly polished surface, like a mirror, redirects most of the light that strikes it.
• Laws of Reflection:
• Angle of incidence = angle of reflection
• The incident ray, normal to the mirror, and the reflected ray all lie in the same plane
• These laws apply to all reflecting surfaces, including spherical ones
• Images formed by plane mirrors are always virtual and erect, the same size as the object, laterally inverted, and as far behind the mirror as the object is in front
• Curved reflecting surfaces, like those of a spoon, can also produce images

Spherical Mirrors

• Spherical mirrors: mirrors whose reflecting surfaces are sections of a sphere
• Concave mirror: a spherical mirror with its reflecting surface curved inward, that is, facing toward the center of the sphere
• Convex mirror: spherical mirror with its reflecting surface curved outwards
• Important Terms:
• Pole (P): The center of the reflecting surface of a spherical mirror
• Center of Curvature (C): The center of the sphere of which the reflecting surface is a part
• Radius of Curvature (R): The radius of the sphere of which the reflecting surface is a part (equal to the distance PC)
• Principal Axis: The straight line passing through the pole and center of curvature
• Principal axis is normal to the mirror at its pole
• Principal Focus (F): The point on the principal axis where rays parallel to the axis converge after reflection (concave mirror) or appear to diverge from (convex mirror)
• Focal Length (f): The distance between the pole and the principal focus
• Small aperture spherical mirrors have a focal length equal to half the radius of curvature: R = 2f. The principal focus lies midway between the pole and center of curvature
• Aperture: The diameter of the reflecting surface of a spherical mirror

Image Formation by Spherical Mirrors

• Concave Mirrors: Nature, position, and size of the image formed depends on the object's position relative to P, F, and C
• Images can be real or virtual, magnified, reduced, or the same size
• Ray Diagrams: used to study image formation, simplified by using only two rays
• Ray parallel to the principal axis: After reflection, passes through the principal focus (concave) or appears to diverge from it (convex)
• Ray passing through the principal focus (concave) or directed towards it (convex): After reflection, emerges parallel to the principal axis
• Ray passing through the centre of curvature (concave/convex): After reflection, reflects back along the same path
• Ray incident obliquely to the principal axis at the pole (P): Reflected obliquely, making equal angles with the principal axis
• Concave Mirror Uses: Torches, search-lights, vehicle headlights, shaving mirrors, dentist mirrors, solar furnaces
• Convex Mirrors: Always give an erect, though diminished, image
• Wider field of view makes them ideal for rear-view mirrors in vehicles

Sign Convention for Reflection by Spherical Mirrors

• New Cartesian Sign Convention: Used to deal with the reflection of light by the sperical mirror
• The pole (P) of the mirror is the orgin
• The principal axis of the mirror is the x-axis (X'X) of the coordinate system
• Object is always placed to the left of the mirror
• All distances are to be measured from the pole of the mirror
• Sign rules:
• Distances to the right of the origin (+ x-axis): positive
• Distances to the left of the origin (- x-axis): negative
• Distances perpendicular to and above the principal axis (+ y-axis): positive
• Distances perpendicular to and below the principal axis (-y-axis): negative
• Mirror Formula: relates object distance (u), image distance (v), and focal length (f)
• 1/v + 1/u = 1/f (Valid for all spherical mirrors, use New Cartesian Sign Convention)
• Magnification (m): ratio of the height of the image (h') to the height of the object (h): m = h'/h
• Also m = -v/u
• Object height is positive, image height should be positive for virtual images and negative for real images
• Negative magnification indicates real image, positive indicates virtual

Refraction of Light

• Refraction: change in direction of light when it passes obliquely from one transparent medium to another
• Light travels at different speeds in different media
• Laws of Refraction:
• The incident ray, refracted ray, and the normal to the interface of the two media all lie in the same plane
• Snell's Law: For a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant: (sin i)/(sin r) = constant
  • This constant value defines the refractive index of the second medium with respect to the first
• Refractive Index: Relates to the relative speed of light in different media
• n21 = (speed of light in medium 1)/(speed of light in medium 2) = v1/v2 (Refractive index of medium 2 with respect to medium 1)
• n12 = (speed of light in medium 2)/(speed of light in medium 1) = v2/v1 (Refractive index of medium 1 with respect to medium 2)
• Absolute Refractive Index: Refractive index of a medium with respect to vacuum
• If medium 1 is vacuum/air, then, n m= c/v, where c is light's speed in air/vacuum and v is light’s speed in the medium
• Optical Density: Ability of a medium to refract light
• Higher Refractive Index = Optically Denser Medium; Lower Refractive Index = Optically Rarer Medium
• Light ray travelling from a rarer medium to a denser medium slows down and bends towards the normal. In reverse, it speeds up and bends away

Refraction by Spherical Lenses

• Lens: Transparent material bound by two surfaces, one or both of which are spherical
• Convex Lens (Converging Lens): Thicker at the middle, converges light rays
• Concave Lens (Diverging Lens): Thicker at the edges, diverges light rays
• Important Terms:
• Centers of Curvature (C1, C2):The centers of each surface is part of a sphere
• Principal Axis: The imaginary straight line passing through the two centers of curvature
• Optical Center (O): The central point of the lens. A light ray passing through it emerges without deviation
• Principal Focus (F): Point on the principal axis where rays parallel to the axis converge (convex) or appear to diverge from (concave)
• Focal Length (f): Distance between the optical center and the principal focus
• Image Formation by Convex Lenses: Nature, position, and relative size depend on the object's position
• Ray diagrams help study image formation:
  • Ray parallel the principal axis: passes through F on the other side (convex) or appears to diverge from F on the same side (concave).
  • Ray passing through F: emerges parallel to the axis.
  • Ray through optical centre: Undeviated.
• Concave Lenses: Always give virtual, erect, and diminished images
• Lens Formula: relates object distance (u), image distance (v), and focal length (f), 1/v - 1/u = 1/f
• Valid for all spherical lenses; use the sign conventions
• Magnification (m): m = h'/h = v/u, where h’is image height
• Power of a Lens: its ability to converge or diverge light rays
• P = 1/f, , where fis the focal length in meters. SI unit is dioptre (D) where 1D = 1m-1
• Convex lens power is positive, concave is negative