Question

can light travel from one medium to another without any change of path

Answer 1

light will change its path if the refractive indexes of the 2 mediums are different. if the refractive indexes of two mediums are same, it will not change its path as its speed wont change.

Answer 2

Yes , The formula for angle of refraction is n1 (sinx)= n2 (siny) , where x and y being angle of incidence and refraction respectively. So here angle of incidence is zero . Sin0=0, hence angle of refraction is also zero.And hence the light travels without any change of path.