Explanation of the Critical Angle
The critical angle is the angle of incidence at which the refracted ray of light becomes parallel to the boundary of the medium. At this angle, the refracted ray no longer passes through the medium but is reflected back into the same medium.

Calculating the Refractive Index of the Medium
We can use the formula n = c/v to calculate the refractive index of the medium, where n is the refractive index, c is the speed of light in vacuum and v is the speed of light in the medium. We know that the speed of light in vacuum is approximately 3 x 10^8 m/s. We can calculate the speed of light in the medium by using the distance traveled and the time taken by the light to cover the distance.

Calculating the Critical Angle
Once we have calculated the refractive index of the medium, we can use the formula sin c = 1/n to calculate the critical angle, where c is the critical angle and n is the refractive index of the medium.

Application to the Given Problem
In the given problem, light takes t1 seconds to travel a distance x cm in vacuum and t2 seconds to travel 10x cm in a medium. We can use the formula v = d/t to calculate the speed of light in the medium, where v is the speed of light in the medium, d is the distance traveled in the medium and t is the time taken by the light to cover the distance. Once we have calculated the speed of light in the medium, we can use the formula n = c/v to calculate the refractive index of the medium. Finally, we can use the formula sin c = 1/n to calculate the critical angle for the medium.