Chapter 33, Problem 33.60CP

(a)

To determine

The validation of relations ${\theta }_{\text{a}}^{\text{B}}={\theta }_{\text{b}}^{\text{A}}$ , ${\theta }_{\text{a}}^{\text{C}}={\theta }_{\text{b}}^{\text{A}}$ and ${\theta }_{\text{b}}^{\text{C}}={\theta }_{\text{a}}^{\text{A}}$.

(b)

To determine

The validation of relation for angle between the ray before it enters the drop at A and after it exits at C is $\Delta =2{\theta }_{\text{a}}^{\text{A}}-4{\theta }_{\text{b}}^{\text{B}}+\pi$

(c)

To determine

The validation of relation for angle between the ray before it enters the drop at A and after it exits at C $\left(\Delta \right)$ in terms of ${\theta }_{\text{a}}^{\text{A}}$ and $n$.

(d)

To determine

The validation of relation ${\cos }^2{\theta }_1=\frac{1}{3}\left(n^2-1\right)$

(e)

To determine

The ${\theta }_1$ and $\Delta$ for violet and red light and also the color red or violet is higher above the horizon.