Critical Angle and Total Internal Reflection

Critical Angle (\(c\)):

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is \(90^\circ\).

• • At this point, the refracted ray just skims along the boundary between the two media.
  • Formula for the critical angle when moving from medium of refractive index \(n_1\) to air (with refractive index \(\approx 1\)):

    \(\sin c = \dfrac{1}{n}\)

    where \(n\) is the refractive index of the denser medium relative to air.

  • More generally, between two media:

    \(\sin c = \dfrac{n_2}{n_1}\)

    where \(n_1 > n_2\).

Key Points:

• • If angle of incidence \(< c\): Refraction occurs.
  • If angle of incidence \(= c\): Ray emerges along the boundary (at \(90^\circ\)).
  • If angle of incidence \(> c\): Total internal reflection occurs.

Total Internal Reflection (TIR):

TIR occurs when light tries to move from a denser medium (higher refractive index, e.g. glass or water) to a less dense medium (lower refractive index, e.g. air).

• • Instead of refracting into the second medium, the light is reflected entirely back inside the denser medium.
  • Thus, no light escapes; it is 100% reflected at the boundary.

Conditions for Total Internal Reflection:

• • Light must travel from a denser medium to a rarer medium.
  • The angle of incidence must be greater than the critical angle.

Applications of Total Internal Reflection:

• Optical fibres: Used in medical endoscopes and telecommunication to transmit light signals with very little loss.
• Prisms: Used in binoculars, periscopes, and cameras to reflect light efficiently without mirrors.
• Sparkling effect in diamonds: Diamonds have a very high refractive index (≈ 2.4), which creates a very small critical angle and enhances total internal reflection, making them sparkle.