Hint: The refraction of light depends on the refractive index of the material.
Step 1: Find the angle of refraction at the first surface.
Any ray entering at an angle i shall be guided along AC if the angle ray makes with a face AC (ϕ) is greater than the critical angle as per the principle of total internal reflection.
So, ϕ+r=90°, therefore, sin ϕ = cos r
⇒ sin ϕ≥1μ
⇒ cos r≥1μ
or 1-cos2r≤1-1μ2
i.e., sin2r≤1-1μ2
Step 2: Find the angle of incidence.
Since, sin i= μ sinr
1μ2sin2 i≤1-1μ2 or sin2 i≤μ2-1
When i=π2, we have the smallest angle ϕ.
Step 3: Find the refractive index of the material.
If that is greater than the critical angle, then all other angles of incidence shall be more than the critical angle.
Thus, 1≤μ2-1
or μ2≥2
⇒ μ≥√2
This is the required result.
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