Light: Reflection and Refraction

• Light helps us to see objects by reflecting off them, which our eyes then perceive.
• Transparent mediums allow light to pass through them.
• Light-related phenomena: image formation via mirrors, twinkling stars, colorful rainbows, light bending via mediums, etc.
• Light travels in straight lines.
• A small light source casts a sharp shadow of an opaque object, further proving light's straight path, this is usually known as a ray of light.

Diffraction of Light

• Light bends around opaque objects in its path, if the object is very small.
• Wave and particle properties of light are reconciled in modern quantum theory

Chapter Focus

• The chapter will address reflection/refraction with straight-line light propagation.
• Reflection via spherical mirrors and refraction of light with real-life applications will be explored.

Reflection of Light

• Most of the light falling on a highly polished surface, such as a mirror undergoes reflection.

Laws of Reflection

• Angle of incidence equals the angle of reflection.
• Incident ray, normal to the mirror (at incidence), and reflected ray all lie in the same plane.
• Reflection laws apply to all reflecting surfaces, including spherical ones.

Image Formation by a Plane Mirror

• Images are always virtual and erect.
• Image size equals object size.
• Image is as far behind the mirror as the object is in front.
• Images are laterally inverted.

Concave Mirrors

• A concave mirror has a reflecting surface curved inwards, toward the sphere's center.
• The surface of spoon curved inwards can be approximated to a concave mirror

Convex Mirror

• A convex mirror has a reflecting surface curved outwards
• The surface of the spoon bulged outwards can be approximated to a convex mirror

Pole

• The center of a spherical mirror's reflecting surface
• It lies on the surface of the mirror is referred to as the pole.
• Usually represented by the letter P.

Center of Curvature

• The reflecting surface of a spherical mirror forms a part of a sphere, and this sphere has a center.
• The center of curvature is not part of the mirror itself and lies outside the reflecting surface.
• Concave mirror's center of curvature lies in front, while a convex mirror's lies behind.
• Represented by the letter C.

Radius of Curvature

• The reflecting surface of a spherical mirror forms a part of a sphere with a radius.
• Radius of curvature relates to the radius of the sphere.
• Represented by the letter R.

Principal Axis

• An imaginary straight line passes through the pole and center of curvature.
• The principal axis is normal to the mirror at its pole.

Principal Focus of a Concave Mirror

• Rays parallel to principal axis converge at a point on the axis after reflecting.
• This point is the principal focus.

Principal Focus of a Convex Mirror

• Rays parallel to the principal axis appear to diverge from a point on the axis after reflecting.
• This point is the principal focus.

Focal Length

• The distance between the pole and principal focus.
• Represented by the letter f.

Aperture

• The diameter of a spherical mirror's reflecting surface.
• Only spherical mirrors with an aperture much smaller than their radius of curvature are considered.
• Distance MN represents the aperture.

Radius of Curvature and Focal Length Relationship

• For spherical mirrors of small apertures, the radius of curvature (R) is twice the focal length (f): R = 2f
• The principal focus lies midway between the pole and curvature center.

Image Formation by Concave Mirrors

• Image's nature/position/size depends on object's position related to P, F, and C.
• Images can be real or virtual, magnified, diminished, or same size.

Ray Diagrams

• Extended objects act as point sources in front of spherical mirrors.
• Two rays are sufficient to locate the image in ray diagrams.
• The intersection of at least two reflected rays indicates the approximate position of the image.
• Incident and reflected rays follow reflection laws, with equal incidence and reflection angles at the point of incidence.

Rules for Tracing Ray Diagrams

• A ray parallel to the principal axis will pass through the principal focus after reflection (concave mirror) or diverge from the principal focus (convex mirror).
• A ray passing through the principal focus of a concave mirror or directed towards the principal focus of a convex mirror will emerge parallel to the principal axis after reflection.
• A ray passing through the center of curvature reflects back along the same path.
• A ray incident obliquely towards the pole (P) is reflected obliquely, maintaining equal angles with the principal axis.

Uses of Concave Mirrors

• Used in torches, search-lights, and vehicle headlights for parallel light beams.
• Shaving mirrors enlarge face image.
• Dentists use concave mirrors for enlarged teeth images.
• Used to concentrate sunlight in solar furnaces.

Image Formation by Convex Mirrors

• Convex mirrors create images when object is at infinity or at a finite distance from the mirror.

Convex Mirror Image Characteristics

• Produces virtual and erect images, though diminished.
• Convex mirrors always give an erect, though diminished, image
• Have a wider field of view due to outward curve.
• Enable drivers to view larger areas than with plane mirrors.

Sign Conventions

• Follow the New Cartesian Sign Convention.
• The pole (P) is the origin.
• The principal axis is the x-axis (X'X)

Sign Conventions - Object

• The object is placed to the left, with light incident from the left.

Sign Conventions - Distances

• All distances parallel to the principal axis are measured from the pole of the mirror.
• Distances to the right of the origin (+ x-axis) are positive.
• Distances to the left of the origin (- x-axis) are negative.
• Distances perpendicular and above the principal axis ( + y-axis) are positive.
• Distances perpendicular and below the principal axis (- y-axis) are negative.

Mirror Formula

• 1 / v + 1 / u = 1 / f
• v is image distance
• u is object distance
• f is focal length
• Valid for all spherical mirrors with all object positions.

Magnification Formula

• m = h' / h
• h' is image height
• h is the object height

Magnification and Distance Formula

• For mirrors the formula is: m = - v / u

Sign of the Image

• Object height is positive (above principal axis).
• Virtual images have positive height.
• Real images have negative height.
• Negative magnification means real image.
• Positive magnification means virtual image.

Real-Life Scenarios Involving Refraction

• Bottom of a water tank appearing raised
• Letters appearing raised under a glass slab
• A pencil appearing displaced while partly immersed in water
• A lemon appearing bigger through water
• When travelling obliquely from one medium to another, the direction of light in the second medium changes, it is known as refraction of light.

Laws of Refraction

• Incident ray, refracted ray, and normal at the interface point all lie in the same plane.
• The ratio of the sine of incidence angle to the sine of refraction angle is constant for a given color and pair of media (Snell's law)
• sin i / sin r = constant

Refractive Index

• The extent of direction change is expressed via the refractive index.
• Refractive index relates to light speed in different media.

Speed of Light

• Light travels at different speeds in different media.
• Fastest in a vacuum (3x10^8 m/s).

Refractive Index of Medium 2

• n21 = (Speed of light in medium 1) / (Speed of light in medium 2) = v1 / v2

Absolute Refractive Index

• When medium 1 is vacuum/air, the refractive index of medium 2 is called the absolute refractive index, represented as nm = c / v.
• c is speed of light in air
• v is speed of light in medium

Optical Density

• Optically denser medium has a larger refractive index than an optically rarer medium.
• Light travels faster in a rarer medium.
• Light slows/bends towards normal when moving from rarer to denser medium and speeds up/bends away when moving from denser to rarer medium

Lenses

• Transparent materials with one or both spherical surfaces.
• Convex lenses converge light, and concave lenses diverge light.

Convex Lens

• Thicker in the middle
• Converges light rays
• Also called converging lens
• Double convex lens

Concave Lens

• Thicker at the edges
• Diverges light rays
• Also called diverging lenses.
• Double concave lens

Centers of Curvature of Lenses

• Lenses have two spherical surfaces shape.
• The centre of these spheres are called centres of curvature of the lens.
• May be represented as C1 and C2.

Principal Axis of Lenses

• An imaginary straight line through the two centres of curvature.

Optical Centre of Lenses

• The central point of a lens, denoted as O.
• Rays through the optical center pass without deviation.

Aperture of Lenses

• Effective diameter of the circular outline of a spherical lens.
• Only thin lenses with small apertures, equidistant from center O are discussed.

Principal Focus of a Convex Lens

• Parallel light rays converge at a point on the principal axis after passing through the lens.
• That point is called is termed the principal focus (F).

Principal Focus of a Concave Lens

• Parallel light rays appear to diverge from a point on the principal axis after passing through the lens.
• That point is known as the principal focus.

Focal Length of Lenses

• The distance from the optical center to the principal focus.
• Denoted as f.
• A lens has two principal foci
• Represented by F1 and F2

Image Formation by Lenses

• Lenses form images via refraction.

Key factors that affect image formation via lenses:

• Nature
• Position
• Relative size

Rules for Image Formation in Lenses

A ray of light from the object, parallel to the principal axis, after refraction from a convex lens, passes through the principal focus on the other side of the lens

• In the case of a concave lens, The ray appears to diverge from the principal focus located on the same side of the lens
• A ray of light passing through a principal focus, after refraction from a convex lens, will emerge parallel to the principal axis
• A ray of light passing through the optical center of a lens will emerge without any deviation.

Sign Conventions for Lenses

• Almost identical to spherical mirrors.
• All measurements originate at the optical center.
• Convex lens has positive focal length; concave lens has negative.

Lens Formula

• 1/v - 1/u = 1/f
• Relates object distance (u), image distance (v), and focal length (f).
• It's general and valid for all lenses, provided sign conventions is considered.

Magnification of Lenses

• m = Height of the image (h') / Height of the object (h).
• m = v/u

Power of a Lens

• A lens's ability to converge/diverge light depends on its focal length.
• Power measured as reciprocal of focal length: P = 1 / f.

Dioptre

• SI unit of lens power.
• Denoted as D.
• If f is in meters, power is in dioptres.
• 1 dioptre is power of lens with 1-meter focal length (1D = 1m⁻¹).
• Convex lens power is positive
• Concave lens power is negative.