Question

Write the necessary conditions for total internal reflection of light.

Hint:

Total internal reflection occurs when the angle of incidence exceeds the critical angle while light moves from a denser to a rarer medium.

Answer 1

Total internal reflection is a phenomenon that occurs when a light ray traveling from a denser medium to a rarer medium strikes the boundary at an angle greater than the critical angle. The necessary conditions for total internal reflection are:
1. The light must travel from a denser medium to a rarer medium: For total internal reflection to occur, the light must be traveling from a medium with a higher refractive index (denser medium) to a medium with a lower refractive index (rarer medium). A typical example is light moving from water (denser) to air (rarer).
2. The angle of incidence must be greater than the critical angle: The critical angle (\( \theta_c \)) is the minimum angle of incidence at which total internal reflection occurs. When the angle of incidence exceeds this critical angle, the light is entirely reflected within the denser medium and does not refract into the rarer medium. The critical angle is given by the formula: \[ \theta_c = \sin^{-1} \left( \frac{n_2}{n_1} \right) \] Where \(n_1\) is the refractive index of the denser medium and \(n_2\) is the refractive index of the rarer medium.
3. The refractive index of the denser medium must be greater than the refractive index of the rarer medium: For total internal reflection to occur, the refractive index of the first medium (denser medium) must be greater than that of the second medium (rarer medium). This ensures that light is not refracted out but instead is entirely reflected back into the denser medium.
In summary, for total internal reflection to take place, light must travel from a denser to a rarer medium, the angle of incidence must be greater than the critical angle, and the refractive index of the denser medium must be greater than that of the rarer medium.