Study Notes on Refraction of Light

Introduction to Refraction

• Refraction is the bending of light as it passes from one medium to another due to a change in its speed.
• Everyday experiences:
  • A straw in lemonade appears bent or broken at the water-air interface.
  • A coin at the bottom of a pool appears shallower than it actually is.

Laws of Refraction

1. First Law: The incident ray, the refracted ray, and the normal to the interface of two transparent media at the point of incidence all lie in the same plane.
2. Second Law (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 the light of a given color and for the given pair of media:
   • $\frac{\sin i}{\sin r} = n$

Speed of Light and Optical Density

• Speed of light varies in different mediums based on their optical density:
  • Air: $3 \times 10^8 \text{ m/s}$
  • Water: $2.25 \times 10^8 \text{ m/s}$
  • Glass: $2 \times 10^8 \text{ m/s}$
  • Diamond: $1.25 \times 10^8 \text{ m/s}$
• Optical Density vs. Mass Density: Material density is mass per unit volume, whereas optical density is a measure of a medium's ability to slow down light. For example, turpentine has a lower mass density than water but a higher optical density.

Behavior of Light Rays

• Rarer to Denser Medium: When light moves from a medium with lower optical density (e.g., Air) to a higher one (e.g., Glass), it slows down and bends towards the normal (i > r).
• Denser to Rarer Medium: When light moves from a medium with higher optical density to a lower one, it speeds up and bends away from the normal (i < r).
• Normal Incidence: If light enters the interface at $90^\circ$ (perpendicularly), its speed changes but its direction does not deviate.

Refractive Index Explained

• Absolute Refractive Index ($n$): The ratio of the speed of light in a vacuum ($c$) to the speed in a medium ($v$):
  • $n = \frac{c}{v}$
• Relative Refractive Index ($n_{21}$): The refractive index of medium 2 with respect to medium 1:
  • $n<em>{21} = \frac{v</em>1}{v_2}$
• Calculations:
  • Water: $n = \frac{3 \times 10^8}{2.25 \times 10^8} \approx 1.33$
  • Glass: $n = \frac{3 \times 10^8}{2 \times 10^8} = 1.5$
  • Diamond: $n = \frac{3 \times 10^8}{1.25 \times 10^8} = 2.4$ (Diamond has a very high refractive index, contributing to its brilliance).

Critical Angle and Total Internal Reflection (TIR)

• Critical Angle ($C$): The specific angle of incidence in a denser medium for which the angle of refraction in the rarer medium is exactly $90^\circ$.
  • For glass, $C \approx 42^\circ$.
  • Relationship: $n = \frac{1}{\sin C}$.
• Conditions for Total Internal Reflection:
  1. Light must travel from a denser medium to a rarer medium.
  2. The angle of incidence ($i$) must be greater than the critical angle ($C$).
• When these conditions are met, light does not refract but is instead entirely reflected back into the denser medium.

Applications of Total Internal Reflection

• Optical Fibres: Used in telecommunications and endoscopy. Light pulses reflect off the walls of the glass fiber via TIR, allowing signals to travel long distances with minimal loss.
• Mirage Phenomenon: Occurs on