Total Internal Reflection (CIE IGCSE Physics)

• Sometimes, when light is moving from a denser medium towards a less dense one, instead of being refracted, all of the light is reflected
  • This phenomenon is called total internal reflection

• Total internal reflection (TIR) occurs when:

The angle of incidence is greater than the critical angle and the incident material is denser than the second material

• Therefore, the two conditions for total internal reflection are:
  • The angle of incidence > the critical angle
  • The incident material is denser than the second material

Critical angle and total internal reflection

• Total internal reflection is utilised in:
  • Optical fibres e.g. endoscopes
  • Prisms e.g. periscopes

Prisms

• Prisms are used in a variety of optical instruments, including:
  • Periscopes
  • Binoculars
  • Telescopes
  • Cameras

   

• They are also used in safety reflectors for bicycles and cars, as well as posts marking the side or edge of roads

• A periscope is a device that can be used to see over tall objects
  • It consists of two right-angled prisms

Reflection of light through a periscope

• The light totally internally reflects in both prisms

Single and double reflection through right-angled prisms

• 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

As the angle of incidence increases it will eventually surplus the critical angle and lead to total internal reflection of the light

• When the angle of incidence is larger than the critical angle, the refracted ray is now reflected
  • This is total internal reflection

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

EXTENDED

• The critical angle, c, of a material is related to its refractive index, n
• The relationship between the two quantities is given by the equation:

• This can also be rearranged to calculate the refractive index, n:

• This equation shows that:
  • The larger the refractive index of a material, the smaller the critical angle
  • Light rays inside a material with a high refractive index are more likely to be totally internally reflected

Step 1: List the known quantities

• • Refractive index of opal, n_o = 1.5
  • Refractive index of diamond, n_d = 2.4

Step 2: Write out the equation relating critical angle and refractive index

Step 3: Calculate the critical angle of opal (c_o)

sin(c_o) = 1 ÷ 1.5 = 0.6667

c_o = sin^–1 (0.6667) = 41.8 = 42°

Step 4: Calculate the critical angle of diamond (c_d)

sin(c_d) = 1 ÷ 2.4 = 0.4167

c_d = sin^–1 (0.4167) = 24.6 = 25°

Step 5: Compare the two values and write a conclusion

• • Total internal reflection occurs when the angle of incidence of light is larger than the critical angle (i>c)
  • In opal, total internal reflection will occur for angles of incidence between 42° and 90°
  • The critical angle of diamond is lower than the critical angle of opal (c_o>c_d)
  • This means light rays will be totally internally reflected in diamond over a larger range of angles (25° to 90°)
  • Therefore, more total internal reflection will occur in diamond hence it will appear to sparkle more than the opal

EXTENDED

• Total internal reflection is used to reflect light along optical fibres, meaning they can be used for
  • Communications
  • Endoscopes
  • Decorative lamps

• Light travelling down an optical fibre is totally internally reflected each time it hits the edge of the fibre

Optical fibres utilise total internal reflection for communications

• Optical fibres are also used in medicine in order to see within the human body

Endoscopes utilise total internal reflection to see inside a patient's body