Total Internal Reflection (Edexcel IGCSE Physics: Double Science)

• 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

The angles of refraction, critical and total internal reflection

The critical angle is different for different materials. Refraction occurs when the angle of incidence is less than the critical angle, and total internal reflection occurs when it is greater

• Total internal reflection is utilised in
  • optical fibres e.g. endoscopes
  • prisms e.g. periscopes

Optical fibres

• 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

Light travelling in an optical fibre

Optical fibres utilise total internal reflection for communications

Structure of an endoscope

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

Prisms

• Prisms are used in a variety of optical instruments, including
  • periscopes
  • binoculars
  • telescopes
  • cameras

• Prisms are also used in safety reflectors for bicycles and cars, as well as posts marking the edges of roads
• A periscope is a device consisting of two right-angled prisms that can be used to see over tall objects

Reflection of light in a periscope

When light travels through a periscope, it totally internally reflects through prisms causing the light to reflect at right angles

• The light totally internally reflects in both prisms

Reflection of light by right-angled 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

Changing the angle of incidence to obtain the critical angle

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

• 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