Mirror Formula and Convex Mirrors

Physics 1 - Preparatory Year Students

• Unit 2: Light
  • Light is a form of energy in the electromagnetic spectrum.
  • The visible spectrum ranges roughly 380 to 780 nm.
  • Theory of Light:
    • Seventeenth-century physicists debated light's nature.
    • Huygens proposed a wave theory.
    • Newton suggested a particle theory (corpuscles).
    • Huygens’ wave theory explained diffraction, interference, and reflection.
    • Newton's particle theory explained reflection and refraction.
  • Speed of Light:
    • The speed of light in a vacuum (c) is 299,792,458 meters per second.
    • Light travels at the speed of light in a vacuum.
    • Light slows down when passing through transparent materials like glass or water, the ratio of c to the speed in the material is the refractive index.

Reflection of Light

• Reflection is the bouncing back of light from a surface.
• Incident Ray: The incoming ray of light.
• Reflected Ray: The outgoing ray of light.
• Normal: The perpendicular to the reflecting surface at the point of reflection.
• Angle of Incidence (i): The angle between the incident ray and the normal.
• Angle of Reflection (r): The angle between the reflected ray and the normal.
• Laws of Reflection:
  • The incident ray, reflected ray, and the normal all lie in the same plane.
  • The angle of incidence equals the angle of reflection.
• Types of Reflection:
  • Specular Reflection: Occurs on smooth surfaces, producing clear reflections (like mirrors).
  • Diffuse Reflection: Occurs on rough surfaces, scattering light in many directions.

Mirrors

• Types of Mirrors:
  • Plane Mirrors: Flat mirrors that produce upright, virtual images of the same size as the object.
  • Concave Mirrors: Spherical mirrors that curve inward; produce real or virtual images depending on object position relative to focal point, real images are inverted, and virtual images are upright
  • Convex Mirrors: Spherical mirrors that curve outward; always produce virtual, upright, and diminished images.

Mirror Formula

• Mirror Formula: 1/f = 1/u + 1/v, where:
  • f = focal length
  • u = object distance
  • v = image distance
• Magnification (m): m = h'/h = -v/u, where:
  • h' = image height
  • h = object height

Image Formation by Mirrors

• Real Images: Formed where light rays actually intersect. Can be projected onto a screen.
• Virtual Images: Formed where light rays appear to originate. Cannot be projected onto a screen.

Refraction of Light

• Refraction: Light bending as it passes from one medium to another due to a change in speed.
• Angle of Incidence: The angle between the incident ray and the normal.
• Angle of Refraction: The angle between the refracted ray and the normal.
• Snell's Law: n₁ sin θ₁ = n₂ sin θ₂, where n₁ and n₂ are the refractive indices of the two media.

Refractive Index

• Refractive Index (n): The ratio of the speed of light in a vacuum to the speed of light in a given material.
• Absolute Refractive Index: The refractive index of a material relative to a vacuum.
• Relative Refractive Index: The refractive index of one material relative to another.

Lenses

• Lens: A curved piece of transparent material that refracts light.
• Types of Lenses:
  • Convex Lenses: Converging lenses that focus light rays.
  • Concave Lenses: Diverging lenses that spread light rays.
• Focal Length (f): The distance from the lens to the focal point where parallel rays converge (convex) or appear to diverge from (concave).
• Lens Formula: 1/f = 1/u + 1/v

Power of a Lens

• Power (P): A measure of a lens' ability to converge or diverge light, expressed in diopters (D). P = 1/f, where f is in meters.