For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index : lies between 2 and √2, is greater than 2, is less than 1, or lies between √2 and 1?

Applying Snell's law, we have
μ = sin[(A+δm)/2] / sin(A/2)
where μ is the refractive index of the prism, A is the refracting angle, and δm is the angle of minimum deviation.
For δm = A, we have
μ = sin A / sin(A/2) = 2cos(A/2)
Since the maximum value of cos(A/2) is 1, the maximum value of μ is 2.
Also, since A must be greater than 0, the minimum value of cos(A/2) is greater than 0, implying μ > 1.
Therefore, the refractive index μ lies between 1 and 2.