Lecture Notes: Refractive Index

Introduction

• Topic: Refractive Index
• Common fear among 10th-grade students regarding numericals in the Light chapter, particularly Snell's law
• Assurance: Full explanation within 15-20 minutes

Key Concept: Reflection and Refraction

• Reflection: Light bouncing back upon hitting a surface
• Refraction: Bending of light when it passes from one medium to another
  • Towards the normal or away from the normal

What is Refractive Index?

• Definition: Ability of a material to bend light
  • Example: Some materials bend light a little, some bend it a lot
• Represented by: n (or sometimes μ)
• Relation with Bending: Higher ability to bend light = Higher refractive index
  • E.g., Diamond (n = 2.42), Glass (n = 1.5), Water (n = 1.33)

Important Properties

1. Refractive Index is Directly Proportional to Bending of Light

   • Higher refractive index = More bending of light

2. Refractive Index is Directly Proportional to Optical Density

   • Higher density = Higher refractive index
   • E.g., Water < Glass < Diamond in terms of density

3. Refractive Index is Inversely Proportional to Speed of Light

   • Higher refractive index = Lower speed of light

Formulae & Snell's Law

• Snell's Law: n = sin(i) / sin(r)
  • n - Refractive index, i - Angle of incidence, r - Angle of refraction
  • Refractive index = n2 / n1 = c1 / c2
    • c1 - Speed of light in medium 1, c2 - Speed of light in medium 2

Types of Refractive Index

1. Absolute Refractive Index: Fixed first medium as vacuum/air
2. Relative Refractive Index: Both media are variable

Numerical Examples

1. Basic: Given i = 30° and r = 60°, find n

   • Solution: n = sin(30) / sin(60) = 1/2 / (√3/2) = 1/√3

2. Complex: Given n(water) / n(air) = 1.5, find speed of light in water

   • Solution: c1 / c2 = 1.5, where c1 is speed in air (~3 x 10^8 m/s)
   • c2 = (3 x 10^8) / 1.5

3. Advanced: Given multiple refractive indices, e.g., n(x)/n(a)=4/3 and n(s)/n(a)=3/2, find n(x)/n(s)

   • Solution: Divide equations to get: n(x)/n(s) = 8/9
   • Homework: Solve the reverse: n(s)/n(x)

Conclusion

• Summary: Understanding of refractive index, Snell's law, and their applications
• Ending note: Engagement and practice, assurance for a better understanding

Additional Resources

• Further reading and numericals available in the Light chapter playlist on the channel