from laws of relection wkt

i=r

the angle between reflected and refracted ray is 90 degrees

so,

r+90+r'=180

r+r'=90

i+r'=90

i=90-r'

sin i=sin (90-r')

sin i=cos r'

from lawsof refraction μ=sin i/sin r

=cos r'/sin i

1/μ=tan r'

sin ^-1 (1/μ)=sin ^-1 (tan r')

which is the critical angle