The refractive index of the medium M in the diagram above is

Answer Details

In the diagram given, the incident ray AO is perpendicular to the surface AB. Therefore, it will pass straight through without deviation. When it reaches the surface BC, it will refract according to Snell's law. We can write:
sin(i)/sin(r) = n
where i is the angle of incidence, r is the angle of refraction, and n is the refractive index of the medium. Since the incident ray is perpendicular to AB, i = 0. We can then simplify the equation to:
sin(r) = 0
This means that the refracted ray is parallel to the surface BC. When it reaches the surface CD, it will once again refract according to Snell's law. We can write:
sin(i)/sin(r) = n
where i is the angle of incidence and r is the angle of refraction. The incident angle i is equal to the angle of reflection, which is 60 degrees in this case. We can then simplify the equation to:
sin(60)/sin(r) = n
Solving for n, we get:
n = sin(60)/sin(r)
The angle of minimum deviation occurs when the refracted ray is symmetric with respect to the incident ray. In other words, the angles of incidence and refraction are equal. Since the incident angle is 60 degrees, the angle of refraction at CD is also 60 degrees. Therefore, we can substitute r = 60 degrees into the equation above to get:
n = sin(60)/sin(60) = 1
The refractive index of the medium M is therefore 1. Answer option (2√3) is incorrect because it is greater than 1, and answer options (1/√3) and (2/√3) are incorrect because they are less than 1. The correct answer is option ( √3).