5.14 Critical Angle

• As the angle of incidence is increased, the angle of refraction also increases until it gets 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:

n₁ sin θ₁ = n₂ sin θ₂

• Where:
  • θ₁ = C 
  • θ₂ = 90°
  • n₁  = n
  • n₂ = 1 (air)

a) Complete the diagram to show the path of the ray beyond X

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

 

b) Calculate the critical angle for the ray at the glass-liquid boundary:

Step 1: Recall Snell's Law and rearrange to make critical angle the subject

n₁ sin θ₁ = n₂ sin θ₂ 

Step 2: Substitute in the known quantities

• n₁ = refractive index of glass cube = 1.45
• n₂ = refractive index of liquid = 1.32
• θ₁ = C
• θ₂ = 90° (The angle of refraction is 90° when at the critical angle)

 

Step 3: Calculate the critical angle