# 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 rod does not cross the curved surface of rod.

$(a)\; n > \frac{1}{\sqrt 2} \\ (b)\;n < \frac{1}{\sqrt 2} \\ (c)\; n > \sqrt 2 \\ (d)\; n < \sqrt 2$

It is required that no ray exits from the curved surface.
This will be automatically fulfilled if minimum r' is more than critical angle.
Angle r' is minimum when r is maximum ie C.
Therefore minimum value of r' is $90-c$
From above condition
$90 ^{\circ} -C > C$
or $C < 45^{\circ}$
$\sin C < \sin 45 ^{\circ}$
$\large\frac{1}{n} < \frac{1}{\sqrt 2}$
$n > \sqrt 2$
Hence c is the correct answer.

edited Jul 21, 2014