Lecture on Total Internal Reflection and Critical Angle

Key Concepts

Total Internal Reflection: Occurs when a light ray traveling from a medium with a higher index of refraction to a lower index of refraction cannot refract anymore; it reflects back entirely.
Critical Angle: The incident angle at which the refracted angle is 90 degrees. Above this angle, total internal reflection occurs.

Incident Ray: Light ray that strikes the boundary between two different media.
Incident Angle (θi): Angle between the incident ray and the normal line.
Reflection: When a ray bounces back into the original medium.
Refraction: When a ray passes and bends through the boundary into another medium.

Law of Reflection: θi = θr
Snell's Law: n1 * sin(θ1) = n2 * sin(θ2)
- n1 and n2 are indices of refraction for the respective media.
- For air, n ≈ 1; for water, n ≈ 1.33; and for diamond, n ≈ 2.42.

Refraction Direction:
- From high n to low n: Bends away from the normal.
- From low n to high n: Bends towards the normal.
Total Internal Reflection Conditions:
- Only occurs from high n to low n.
- Happens when the incident angle exceeds the critical angle.

Critical Angle for Air and Water:
- Using n1 = 1 (air) and n2 = 1.33 (water):
- Critical angle = sin⁻¹(1/1.33) ≈ 48.75°
Incident Angle Greater than Critical Angle:
- Example with incident angle = 50° for air and water:
- No refraction occurs since sin(θ2) cannot exceed 1.
Critical Angle Between Glass and Water:
- Indices: Water n = 1.33, Glass n = 1.5
- Critical angle = sin⁻¹(1.33/1.5) ≈ 62.5°
Finding Index of Refraction for Solid:
- Given critical angle = 40° and air n = 1:
- Index = 1/sin(40°) ≈ 1.56

Total internal reflection is significant in optics, used in fiber optics and other technologies.
The critical angle is crucial for designing lenses and understanding light behavior at material interfaces.

Note: Always ensure the refraction angle is 90° when dealing with critical angle problems.