Afiber-optic cable (n = 1.53) is submerged in water (n = 1.33). predict whether light will be refracted or whether it will undergo total internal reflection if the angle of incidence is between 65° and 70°.

Total internal refraction occurs when a ray of light meets the following conditions. 
1. light falls from an optically dense material to a less dense material. 
2. The angle of incident in the denser media must be greater than the critical angle. 

In the case above the fiber-optic is optically denser than water. Since the light is incident to fiber-optic-water interface, then one condition is fulfilled.
Checking the other condition we carry out the calculation below;

n1sinФ1=n2sinФ2
where c ⇒critical angle  
1.53 sinc = 1.33 sin 90
sinc =0.86928
   c = 60.37° 

The angle of incident is (65°-70°) is greater than critical angle. 
With certainty, there would be no refraction. Total internal reflection would occur.