Chapter 39, Problem 80AP

(a)

To determine

To show: The speed of light measured in laboratory frame is given by $\frac{c}{n}\left(\frac{1+\frac{nv}{c}}{1+\frac{v}{nc}}\right)$.

(b)

To determine

To show: The speed of light measured in laboratory frame for $\left(v<<c\right)$ is given by $u=\frac{c}{n}+v-\frac{v}{n^2}$.

(c)

To determine

To explain: The argument for or against the view that is expect the result to be $u=\frac{c}{n}+v$ according to the Galilean transformation and that presence of term $-\frac{v}{n^2}$ represents a relativistic effect appearing even at non-relativistic speeds.

(d)

To determine

The speed $u$ in the limit as the speed of water approaches $c$.