Devise straightforward experiments to measure the speed of light in a given glass using (a) Snell’s law; (b) total internal reflection; (c) Brewster’s law

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media.

Snell’s law is given as: $n_a\sin {\theta }_a=n_b\sin {\theta }_b$

So, we measure the angles${\theta }_a$ and${\theta }_b$ and$n_a$ is the refractive index of air which is 1 . After that, you should calculate$n_b$ for the glass from Snell’s law.

Finally, we can get the speed of light into the glass v using equation $v=\frac{c}{n_b}$

From the total reflection, the critical angle is given in the form of $\sin {\theta }_{crit}=\frac{n_b}{n_a}$

Measure the critical angle and we have$n_a=1$ . And from the above equation, calculate$n_b$ and finally find v from equation in the form:

$v=\frac{c}{n_b}$

For Brewster’s law, the polarized angle is given as

$\tan {\theta }_p=\frac{n_b}{n_a}$

Measure the polarized angle and we have . And from the above equation calculate and finally find from equation

Hence, from Snell’s law first, find the refractive index of the glass then measure v from $v=\frac{c}{n_b}$. From total internal reflection, calculate $n_b$from $\sin {\theta }_{crit}=\frac{n_b}{n_a}$then find v from $v=\frac{c}{n_b}$. From Brewster’s law, calculate $n_b$from $\tan {\theta }_p=\frac{n_b}{n_a}$then find from$v=\frac{c}{n_b}$ .