What should be the value of refractive index n of a glass rod placed in air, so that the light entering through the flat surface of the rod does not cross the curved surface of the rod?

Explanation

It is required that all possible `r'` should be more than critical angle. This will be automatically fulfilled if minimum `r'` is more than critical angle
Angle `r'` is minimum when `r` is maximum i.e `C` (why ?) Therefore the minimum value of `r'` is `90-C`
From condition `(A):`
`90^(@) - C gt C` or `C lt 45^(@)`
`sin C lt sin 45^(@), (1)/(n) lt (1)/(sqrt(2))` or `n gt sqrt(2)`