A beam of light is incident at 60° on a planesurface. The reflected and refracted rays areperpendicular to each other, then refractive indexof the surface is:

The problem involves the laws of reflection and refraction (also known as Snell's law).

Step 1: Understand the problem A beam of light is incident at an angle of 60° on a plane surface. The reflected and refracted rays are perpendicular to each other. We need to find the refractive index of the surface.

Step 2: Use the laws of reflection and refraction According to the law of reflection, the angle of incidence is equal to the angle of reflection. So, the angle of reflection is also 60°.

Since the reflected and refracted rays are perpendicular to each other, the angle of refraction is 90° - 60° = 30°.

Step 3: Apply Snell's law Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocity of light in the original medium to the velocity of light in the refracted medium. This ratio is also equal to the refractive index (n) of the second medium with respect to the first.

So, n = sin(i) / sin(r) = sin(60°) / sin(30°) = √3 / 0.5 = 2√3.

Therefore, the refractive index of the surface is 2√3.