A ray falls on a prism`ABC(AB=BC)`and travels as shown in adjoining figure.The minimum refraction index of the prism material should be -

Explanation

To find the minimum refractive index of the prism material, we can follow these steps:

### Step 1: Understand the Geometry of the Prism
Given that the prism ABC has sides AB = BC, we can infer that it is an isosceles prism. The light ray is incident on face AC and undergoes total internal reflection at point D on face AB.

### Step 2: Identify the Incident Angle
Since the ray is incident on face AB at point D, we note that the angle of incidence (i) at this point is 45 degrees. This is important because total internal reflection occurs when the angle of incidence is greater than the critical angle.

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