Question

The refractive index of a certain glass is 1.66. For what incident angle is light reflected

Answer 1

If light is moving inside the glass, it will be reflected when the angle of incidence is above the critical angle of the material, which is given by
$\theta_c = \arcsin ( \frac{n_a}{n_g} )$
where
$n_a = 1.00$ is the refractive index of air
$n_g = 1.66$ is the refractive index of this type of glass

If we plug the numbers into the equation, we find
$\theta_c = \arcsin ( \frac{1.00}{1.66} ) = \arcsin (0.602) =37.0^{\circ}$
So, light will be reflected inside the glass when the angle is equal or greater than this value.