The essential condition for total internal reflection to occur is:

The correct answer is Option (1) → angle of incidence \( i \) > critical angle \( i_c \)

For light going from a denser to a rarer medium, Snell’s law gives \( \sin r = \frac{n_1}{n_2}\sin i \), with \( n_1 \gt n_2 \). The largest possible \( \sin r \) is 1, reached at \( i = i_c \) (the critical angle). For \( i \gt i_c \), \( \sin r \) would have to exceed 1, which is impossible, so no light is refracted and the whole of it is totally reflected.

Why the other options are incorrect

• Option (2) \( i \lt i_c \) — Incorrect. Part of the light is refracted and only a part is reflected.

• Option (3) \( i = i_c \) — Incorrect. At the critical angle the refracted ray just grazes the surface (angle of refraction \( 90^\circ \)); reflection becomes total only beyond it.

• Option (4) \( i = 90^\circ \) — Incorrect. This is only one particular angle, and it is not essential; total internal reflection occurs for every angle larger than \( i_c \).

NCERT (2026-27):
Total Internal Reflection – “… If the angle of incidence is increased still further (e.g., the ray AO₄), refraction is not possible, and the incident ray is totally reflected. This is called total internal reflection. … The angle of incidence corresponding to an angle of refraction 90°, say ∠AO₃N, is called the critical angle (i_c) for the given pair of media. … For values of i larger than i_c, Snell’s law of refraction cannot be satisfied, and hence no refraction is possible.”