The question asks for the minimum refractive index of the material of the prism, given that a ray of light is incident normally on one of the faces and undergoes total internal reflection from the hypotenuse.

To understand the answer, we need to have some knowledge of total internal reflection. Total internal reflection occurs when a ray of light traveling in a denser medium approaches the interface with a less dense medium at an angle of incidence greater than the critical angle. At the critical angle, the angle of refraction becomes 90 degrees and the refracted ray is completely reflected back into the denser medium.

In the case of the isosceles prism, the ray of light is incident normally, meaning it approaches the interface perpendicular to it. Since the angle of incidence is 0 degrees, the ray will always undergo total internal reflection from the hypotenuse. This means that the critical angle for the prism is 90 degrees.

The refractive index of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium. The higher the refractive index, the slower light travels in that medium.

To determine the minimum refractive index of the prism`s material, we need to find the material with a critical angle of