We first apply Snell's Law to the upper surface of the fiber and find the condition for total internal internal reflection.
Total internal reflection occurs when Snell's Law
fails because of the fact that cannot be larger than . If we take medium to be the optical fiber and medium to be free space, then and . So, Snell's Law will fail when
Now, from the right triangle in the diagram, we see that an application of Snell's Law to the leftmost surface of the fiber gives
So, light will stay in the fiber when
So, the condition for total internal reflection is
Therefore, answer (B) is correct.