Step 1: Understanding the Concept:
Brewster's Law gives the relationship between the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection.
For unpolarized incident light, the light reflected at this specific angle (called Brewster's angle or the polarizing angle, \(\theta_p\)) is completely plane-polarized.
Step 2: Key Formula or Approach:
At the polarizing angle \(\theta_p\), the angle between the reflected ray and the refracted ray is exactly \(90^\circ\).
From Snell's law:
\[ \mu = \frac{\sin \theta_i}{\sin \theta_r} \]
Substituting \(\theta_i = \theta_p\). Since the reflected and refracted rays are perpendicular, \(\theta_p + 90^\circ + \theta_r = 180^\circ \implies \theta_r = 90^\circ - \theta_p\).
Step 3: Detailed Explanation:
Substitute \(\theta_r\) into Snell's law:
\[ \mu = \frac{\sin \theta_p}{\sin (90^\circ - \theta_p)} \]
Since \(\sin (90^\circ - \theta_p) = \cos \theta_p\):
\[ \mu = \frac{\sin \theta_p}{\cos \theta_p} \]
\[ \mu = \tan \theta_p \]
Step 4: Final Answer:
The correct relation representing Brewster's Law is \(\mu = \tan \theta_p\).