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

`mu=(sini)/(sinr)rArrsinr=(sini)/(mu)`
Now, `r^(') gt` cirtical angle
`sin r' gt 1/mu`
`sin[90^@-r] gt (1)/(mu)`
`cos r gt (1)/(mu)`
`sqrt(1-sin^(2)r) gt (1)/(mu)`
`sqrt(1-(sin^(2)i)/(mu^(2))) gt (1)/(mu)`
`mu^(2)-sin^(2)i gt 1`
`mu gt sqrt(1+sin^(2)i)`
`i_(max)=90^@`, so `mu gt sqrt(1+sin^(2)90^@)`
`mu gt sqrt(2)`