In one line
The critical angle is the angle of incidence in the denser medium for which the refracted ray just grazes the boundary, and for any larger angle the light is totally reflected back into the denser medium.
Explained simply
Look up from under water in a swimming pool: beyond a certain slant you cannot see the sky, only a mirror-like reflection of the pool floor. That slant is the critical angle; beyond it light cannot escape the water at all.
Technically, when light goes from a medium of higher refractive index \(n_1\) to lower index \(n_2\), it bends away from the normal. At the critical angle \(\theta_c\) the angle of refraction becomes 90°. For \(\theta > \theta_c\) there is no refracted ray and all the light reflects: this is total internal reflection (TIR).
How it works
- Snell's law: \(n_1 \sin\theta_1 = n_2 \sin\theta_2\).
- Since \(n_1 > n_2\), \(\theta_2 > \theta_1\): the ray bends away from the normal.
- Increase \(\theta_1\) until \(\theta_2 = 90°\); then \(\theta_1 = \theta_c\) and \(n_1\sin\theta_c = n_2\).
- For \(\theta_1 > \theta_c\), \(\sin\theta_2\) would have to exceed 1, which is impossible, so all light reflects.
- Two conditions for TIR: (i) light must travel from denser to rarer medium (\(n_1 > n_2\)); (ii) angle of incidence must exceed the critical angle.
Key formula
\(\sin\theta_c = \dfrac{n_2}{n_1}\), where \(\theta_c\) is the critical angle, \(n_1\) the refractive index of the denser medium (fibre core) and \(n_2\) that of the rarer medium (cladding). Refractive indices have no unit.
Quick example
Core \(n_1 = 1.50\), cladding \(n_2 = 1.45\): \(\sin\theta_c = 1.45/1.50 = 0.9667\), so \(\theta_c \approx 75.2°\). Light inside the core must hit the core-cladding boundary at more than 75.2° from the normal to stay trapped.
Common mistakes
- Writing \(\sin\theta_c = n_1/n_2\); the ratio must be less than 1, so it is \(n_2/n_1\).
- Saying TIR happens from rarer to denser medium.
- Measuring the angle from the surface instead of from the normal.
How MU asks it
Asked as "Define critical angle and state conditions for TIR" (3 marks) or as the first step of the numerical aperture derivation. For numericals, always state the formula, substitute, and give the angle in degrees.