Chapter 26 - Geometrical Optics - Problems and Conceptual Exercises - Page 942: 64

a) 1.4 b) $n$ decreases

We know that $n=\frac{n_{air}sin\theta}{sin[tan^{-1}(sin\theta)]}$ We plug in the known values to obtain: $n=\frac{(1.00)sin77^{\circ}}{sin[tan^{-1}(sin77^{\circ})]}$ $n=1.4$ Thus, the minimum value of n is $1.4$ (b) We know that $n=\frac{n_{air}}{sin\theta_c}$ The above equation shows that if $\theta_c$ increases, then $n$ decreases.