• Snell’s law relates the angle of incidence to the angle of refraction, it is given by:

n1?sin?θ1?=?n2?sin?θ2

• Where:
  • n1?= the refractive index of material 1
  • n2?= the refractive index of material 2
  • θ1?= the angle of incidence of the ray in material 1
  • θ2?= the angle of refraction of the ray in material 2

   

• θ1?and?θ2?are always taken from the?normal
• Material 1 is always the material in which the ray goes through?first
• Material 2 is always the material in which the ray goes through?second

• 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?θc

   

• This angle can be found using the formula:

• This can easily be derived from Snell’s law where:
  • θ1?=?θc
  • θ2?= 90°
  • n1?>?n2

   

• 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 > the critical angle
  • The refractive index?n1?is greater than the refractive index?n2

   

(i)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 (or 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

(ii)Step 1: Write down the known quantities

• Refractive index of glass,?n1?= 1.489 (from previous worked example)
• Refractive index of liquid =?n2
• Angle of incidence / critical angle,?θ1?=?θc?= 65°
• Angle of refraction,?θ2?= 90°

Step 2: Write out Snell’s Law or the equation for critical angle

Step 3: Calculate the refractive index of the liquid