A ray of light is incident normally on one of the faces of right angled isosceles prism as shown below. It undergoes total internal reflection from hypotenuse. Which one of the following is the minimum refractive index of the material of the prism?

A ray incident normally on one face of a right-angled isosceles prism enters without deviation. Due to the prism's geometry (angles of 45, 90, 45), the ray strikes the hypotenuse at an angle of incidence (θ) of 45 [t1, t8]. For total internal reflection (TIR) to occur, the angle of incidence must be greater than or equal to the critical angle (θc) [t2, t7]. The relationship is defined by Snell's law as sin θc = 1/n, where n is the refractive index of the prism relative to air [c3, t6]. To achieve TIR at 45, we require sin 45 ≥ 1/n, which simplifies to n ≥ 1/sin 45 [t1, t4]. Since sin 45 = 1/√2, the minimum refractive index n must be √2, which is approximately 1.414 [t4, t10]. Thus, 1.414 is the threshold value required for the ray to be totally reflected.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > Activity 9.10 > p. 148