AQA A Level Physics复习笔记3.5.2 Snell's Law

• 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