When light travels from a medium with greater refractive index 
to a medium with smaller refractive index 
, there exists an angle (called critical angle) above which the light is totally reflected, and the value of this angle is given by
In this problem, we know that the critical angle is
, so we can find the ratio between the refractive indices of the two mediums:
and since the second medium is air (n=1.00), the refractive index of the first medium is
In the second part of the problem, we have light entering from air (
) at angle of incidence of 
, into the second medium with 
. By using Snell's law, we can find the angle of refraction of the light inside the medium:
In this problem, we know that the critical angle is
and since the second medium is air (n=1.00), the refractive index of the first medium is
In the second part of the problem, we have light entering from air (