Light- Reflection and Refraction

Introduction to Light

• Light is defined as a form of energy that enables us to see objects.
• Luminous Objects: Objects that emit their own light, such as the Sun, lamps, and candles.
• Non-Luminous Objects: Objects that do not emit light, such as tables and chairs. We see them because they reflect light from luminous objects into our eyes.
• Nature of Light: Light rays consist of electromagnetic waves. These waves do not require any material medium (solid, liquid, or gas) for propagation.

Reflection of Light

• Definition: The process of sending back light rays that fall on the surface of an object is called REFLECTION of light.
• Best Reflector: Silver metal is considered one of the best reflectors of light.
• Plane Mirrors: These are the mirrors commonly used on dressing tables in homes.
• Ray of Light: The straight line along which light travels.
• Beam of Light: A bundle of light rays.

Laws of Reflection and Image Types

• Applicability: The laws of reflection apply to all types of reflecting surfaces, including spherical surfaces.
• Laws of Reflection:     1. The angle of incidence is equal to the angle of reflection ($i = r$).     2. The incident ray, the reflected ray, and the normal to the mirror at the point of incidence all lie in the same plane.
• Image Formation: An image is formed when light rays coming from an object meet (or appear to meet) at a point after reflection from a mirror or refraction through a lens.
• Real Images:     - Formed when rays of light actually meet at a point after reflection or refraction.     - These images can be formed on a screen and seen with the eyes.
• Virtual Images:     - Formed when the outgoing rays from an object do not actually meet but appear to meet at a point in or behind the optical device.     - They cannot be formed on a screen.     - A plane mirror always forms virtual images.

Characteristics of Images Formed by Plane Mirrors

• Images are always virtual and erect.
• The size of the image is always equal to the size of the object.
• The image is laterally inverted.
• The image is as far behind the mirror as the object is in front of it.
• Lateral Inversion: A phenomenon where the right side of the object appears to be the left side of the image, and the left side appears to be the right side.

Spherical Mirrors

• Definition: A mirror whose reflecting surface is curved inwards or outwards.
• Concave Mirror: A spherical mirror where reflection takes place at the concave or "bent-in" surface.
• Convex Mirror: A spherical mirror where reflection takes place at the convex or "bent-out" surface.

Terminology of Spherical Mirrors

• Center of Curvature ($C$):     - The center of the sphere of which the mirror's reflecting surface is a part.     - It is not part of the mirror itself; it lies outside the reflecting surface.     - For a concave mirror, it lies in front.     - For a convex mirror, it lies behind the mirror.
• Radius of Curvature ($R$): The radius of the sphere of which the reflecting surface of the mirror forms a part.
• Pole ($P$): The center point of the spherical mirror surface.
• Principal Axis: The straight line passing through the pole ($P$) and the center of curvature ($C$).
• Aperture of the Mirror: The portion of the mirror where reflection actually occurs; it represents the size of the mirror.

Principal Focus and Focal Length

• Principal Focus ($F$):     - Concave Mirror: The point on the principal axis where rays parallel to the axis intersect after reflection.     - Convex Mirror: The point on the principal axis from which rays parallel to the axis appear to diverge after reflection.
• Focal Length ($f$): The distance between the pole and the principal focus.
• Mathematical Relationship: The principal focus lies midway between the pole and the center of curvature, given by the formula:
  $R = 2f$

Rules for Obtaining Images Formed by Spherical Mirrors

• Rule 1: A ray of light parallel to the principal axis passes through the principal focus (for concave) or appears to diverge from the focus (for convex) after reflection.
• Rule 2: A ray passing through the center of curvature (concave) or directed toward it (convex) is reflected back along the same path. This occurs because the ray hits the mirror along the normal to the reflecting surface.
• Rule 3: A ray passing through the principal focus (concave) or directed toward it (convex) becomes parallel to the principal axis after reflection.
• Rule 4: A ray incident obliquely to the principal axis toward the pole ($P$) is reflected obliquely. The incident and reflected rays follow the laws of reflection, making equal angles with the principal axis.

Image Formation by Concave Mirrors

• The nature, position, and size of the image depend on the position of the object relative to $P$, $F$, and $C$. Possible object positions include:     1. Between pole $P$ and focus $F$.     2. At the focus $F$.     3. Between focus $F$ and center of curvature $C$.     4. At the center of curvature $C$.     5. Beyond center of curvature $C$.     6. At infinity.
• Uses of Concave Mirrors:     - Shaving mirrors.     - Reflectors in car headlights, hand torches, and table lamps.     - Large concave mirrors are used in solar energy fields to focus sunlight onto objects to be heated.

Image Formation by Convex Mirrors

• Regardless of the object's position, the image formed by a convex mirror is always:     - Behind the mirror.     - Virtual and erect.     - Smaller than the object (diminished).
• Nature/Fidelity: Convex mirrors have their focus and center of curvature behind the mirror; light rays shown behind are virtual.
• Uses of Convex Mirrors: Rear-view mirrors in automobiles. They provide an erect, highly diminished image, which allows for a wide-field view of traffic.

New Cartesian Sign Convention

• Reflection follows a set of conventions where the pole ($P$) is the origin and the principal axis is the x-axis ($X'X$).
• The object is always placed to the left of the mirror (light travels from left to right).
• Distances parallel to the principal axis are measured from the pole.
• Distances measured to the right of the origin ($+x$-axis) are positive.
• Distances measured to the left of the origin ($-x$-axis) are negative.
• Distances measured perpendicular to and above the principal axis ($+y$-axis) are positive.
• Distances measured perpendicular to and below the principal axis ($-y$-axis) are negative.

Mirror Formula and Magnification

• Mirror Formula: Relationships between image distance ($v$), object distance ($u$), and focal length ($f$):
  $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
• Magnification ($m$): The ratio of the height of the image ($h_1$) to the height of the object ($h_2$):
  $m = \frac{h_1}{h_2}$
• Magnification is also related to object and image distances:
  $m = -\frac{v}{u}$

Refraction of Light

• Definition: The bending of light when it passes from one medium to another of different density.
• Cause: Refraction occurs because the speed of light is different in different media.
• Optically Rarer Medium: Medium in which the speed of light is faster (e.g., air).
• Optically Denser Medium: Medium in which the speed of light is slower (e.g., glass is denser than air or water).
• Bending Rules:     - Rarer to Denser medium: Light bends towards the normal.     - Denser to Rarer medium: Light bends away from the normal.

Refraction through a Rectangular Glass Slab

• Process: Light ($AO$) enters glass at point $O$, bends towards normal (refracted ray $OB$), and exits at point $B$ into air, bending away from normal (emergent ray $BC$).
• Key Properties:     - The emergent ray is parallel to the incident ray because the bending at the two parallel surfaces ($PQ$ and $SR$ interfaces) is equal and opposite.     - Angle of incidence ($i$) = Angle of emergence ($e$).
• Normal Incidence: If a ray is incident normally to the interface, there is no bending, and it travels straight.

Laws of Refraction (Snell’s Law)

• Law 1: The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane.
• Law 2 (Snell’s Law): The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for light of a given color and a given pair of media:
  $\frac{\sin(i)}{\sin(r)} = \text{constant}$
• Refractive Index: The constant value in Snell’s law represents the refractive index of the second medium with respect to the first.

Refractive Index and Speed of Light

• The refractive index ($n_{21}$) of medium 2 with respect to medium 1 is the ratio of light speeds:
  $n_{21} = \frac{v_1}{v_2}$
• The refractive index ($n_{12}$) of medium 1 with respect to medium 2:
  $n_{12} = \frac{v_2}{v_1}$
• Absolute Refractive Index ($n_m$): If medium 1 is vacuum or air, the refractive index of medium 2 is considered relative to vacuum ($c$ being the speed of light in air):
  $n_m = \frac{c}{v}$

Spherical Lenses

• Definition: A piece of transparent glass bound by two spherical surfaces.
• Convex Lens: Bulges outward, thick at center, thin at edges. It converges light rays and is called a converging lens.
• Concave Lens: Bulges inward, thin in middle, thick at edges. It diverges light rays and is called a diverging lens.
• Lens Terminology:     - Centers of Curvature ($C_1, C_2$): The centers of the spheres forming the lens surfaces.     - Principal Axis: Imaginary line through the two centers of curvature.     - Optical Centre ($O$): The central point of the lens through which light passes without deviation.     - Aperture: The effective diameter of the circular outline of the lens.     - Principal Focus ($F$): Point where parallel rays converge (convex) or appear to diverge from (concave).     - Focal Length ($f$): Distance from the optical center to the principal focus.

Image Formation by Lenses

• Object positions for Convex Lenses study:     - At infinity     - Beyond $2F_1$     - At $2F_1$     - Between $F_1$ and $2F_1$     - At focus $F_1$     - Between focus $F_1$ and optical center $O$
• Concave Lens Character: Always provides a virtual, erect, and diminished image regardless of the object's position.

Lens Formula, Magnification, and Power

• Sign Convention for Lenses:     - Distances measured from optical center ($O$).     - Same direction as incident light = positive.     - Opposite direction to incident light = negative.     - Upward/perpendicular to principal axis = positive.     - Downward/perpendicular to principal axis = negative.
• Lens Formula:
  $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
• Magnification ($m$): Ratio of image height to object height:
  $m = \frac{v}{u}$
• Power of a Lens ($P$):     - Defined as the reciprocal of the focal length ($f$) in meters.     - $P = \frac{1}{f}$     - The SI unit of power is the diopter ($D$).     - $1\,D = 1\,m^{-1}$     - Convex lens power: Positive.     - Concave lens power: Negative.