Question

State the two conditions under which total internal reflection occurs.

Hint:

Remember the two conditions for total internal reflection: \[ \boxed{ \text{Denser Medium} \rightarrow \text{Rarer Medium} } \] and \[ \boxed{ i>C } \] where \(C\) is the critical angle. A simple way to remember: \[ \boxed{ \text{DRC Rule} } \] \[ \text{D} \rightarrow \text{Denser to Rarer}, \qquad \text{C} \rightarrow \text{Incidence angle greater than Critical angle}. \]

Answer 1

Concept: Total internal reflection (TIR) is the phenomenon in which a ray of light travelling from one medium to another is completely reflected back into the denser medium without suffering any refraction. This phenomenon occurs only under certain specific conditions. If these conditions are not satisfied, the light ray undergoes ordinary refraction instead of total internal reflection. Condition 1: The light must travel from an optically denser medium to an optically rarer medium.
Suppose the refractive indices of the two media are \[ n_1 \quad \text{and} \quad n_2, \] where \[ n_1>n_2. \] Then the light ray must travel from medium \(1\) (denser medium) to medium \(2\) (rarer medium). Examples:
• Glass \(\rightarrow\) Air
• Water \(\rightarrow\) Air
• Diamond \(\rightarrow\) Air If light travels from a rarer medium to a denser medium, total internal reflection cannot occur. Hence, the first condition is \[ \boxed{ \text{Light must travel from an optically denser medium to an optically rarer medium.} } \] Condition 2: The angle of incidence in the denser medium must be greater than the critical angle.
The critical angle \(C\) is defined as the angle of incidence in the denser medium for which the angle of refraction in the rarer medium becomes \[ 90^\circ. \] Thus, \[ \boxed{ i=C \quad \Rightarrow \quad r=90^\circ } \] For total internal reflection to occur, \[ \boxed{ i>C } \] where
• \(i\) is the angle of incidence,
• \(C\) is the critical angle. If \[ i<C, \] ordinary refraction takes place. Therefore, the second condition is \[ \boxed{ \text{The angle of incidence must be greater than the critical angle.} } \] Hence, the two necessary conditions for total internal reflection are:
• The light ray must travel from an optically denser medium to an optically rarer medium.
• The angle of incidence in the denser medium must be greater than the critical angle for the pair of media.