Ray Optics Lecture Notes

1. Introduction to Reflection

• Reflection Definition: When a ray of light falls on a mirror and bounces back into the same medium.

• Key Components:

  • Incident Ray: The incoming ray that strikes the surface
  • Point of Incidence: The point where the incident ray meets the surface
  • Normal: A perpendicular line drawn at the point of incidence
  • Reflected Ray: The ray that bounces back
  • 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:

  1. Angle of incidence (i) is equal to the angle of reflection (r)
  2. The incident ray, the reflected ray, and the normal all lie in the same plane

2. Introduction to Refraction

• Refraction Definition: The bending of light as it passes from one medium to another, changing its speed.

• Key Components:

  • Incident Ray: The incoming ray entering another medium
  • Point of Incidence: Where the ray enters the new medium
  • Normal: A perpendicular line drawn at the point of incidence
  • Refracted Ray: The ray that bends inside the new medium
  • Angle of Incidence (i): The angle between the incident ray and the normal
  • Angle of Refraction (r): The angle between the refracted ray and the normal

• Laws of Refraction (Snell's Law):

  • Refractive Index (n) = sin(i) / sin(r)
  • Snell's Law: n = c / v = λ₀ / λₘ
    • c is the speed of light in vacuum
    • v is the speed of light in the medium
    • λ₀ is the wavelength in vacuum
    • λₘ is the wavelength in the medium
  • Note: Frequency (f) does not change during refraction

3. Refractive Indices

• Refractive Index (n) values:
  • Water: 1.33
  • Glass: 1.5
  • Air/Vacuum: 1

4. Important Concepts in Refraction

• Frequency and Wavelength Relationship: Frequency remains constant; speed and wavelength change.
• Refractive Index and Wavelength Relation: Inversely proportional. Higher wavelength in vacuum, lower refractive index.
• Examples:
  • Red light has a longer wavelength and lower refractive index compared to blue light.
  • Blue light has a shorter wavelength and higher refractive index.

5. Lateral Shift

• Lateral Displacement Definition: When light passes through a parallel-sided slab (like glass), it gets laterally displaced.
• Formula for Lateral Displacement (D):
  • D = T * (sin(i - r)) / cos(r)
  • T: Thickness of the slab
  • i: Angle of incidence
  • r: Angle of refraction

6. Apparent Depth and Real Depth

• Apparent Depth: When looking into a medium (like water), objects appear shallower than they are.
• Formula: n = Real Depth / Apparent Depth
• Example Calculation:
  • Given: Velocity in glass = 2 × 10^8 m/s, Velocity in air = 3 × 10^8 m/s
  • Find: How much an ink dot appears raised when covered by a glass plate of 6 cm.
  • Solution: Using D = T (1 - 1/n), where T is the thickness and n is the refractive index

7. Practice Problems

• Various examples were discussed to apply the principles outlined above, including calculations of lateral displacement, refractive index, angle of incidence, and angle of refraction.