4.8.2 Total Internal Reflection

• As the angle of incidence is increased, the angle of refraction also increases until it gets closer to 90°
• When the angle of refraction is exactly 90° the light is refracted along the boundary
  • At this point, the angle of incidence is known as the critical angle C

• This angle can be found using the formula:

• This can easily be derived from Snell’s law where:
  • θ₁ = C 
  • θ₂ = 90°
  • n₁  = n
  • n₂ = 1 (air)

• Total internal reflection (TIR) occurs when:

The angle of incidence is greater than the critical angle and the incident refractive index n₁ is greater than the refractive index of the material at the boundary n₂

• Therefore, the two conditions for total internal reflection are:
  • The angle of incidence, θ₁ > the critical angle, C
  • Refractive index n₁ > refractive index n₂ (air)

Step 1: Draw the reflected angle at the glass-liquid boundary

• • When a light ray is reflected, the angle of incidence = angle of reflection
  • Therefore, the angle of incidence (and reflection) is 90° – 25° = 65°

Step 2: Draw the refracted angle at the glass-air boundary

• • At the glass-air boundary, the light ray refracts away from the normal
  • Due to the reflection, the light rays are symmetrical to the other side

Step 3: Calculate the critical angle

• • The question states the ray is “totally internally reflected for the first time” meaning that this is the lowest angle at which TIR occurs
  • Therefore, 65° is the critical angle