Ordinary light incident on a glass slab at the polarizing angle, suffers a deviation of \(22^{\circ}\). The value of angle of refraction in this case is (A) \(44^{\circ}\) (B) \(34^{\circ}\) (C) \(22^{\circ}\) (D) \(11^{\circ}\)

When light passes through a transparent medium like glass, the polarizing angle (also known as Brewster's angle) is the angle of incidence at which the reflected light becomes completely polarized. At this angle, the reflected ray and transmitted ray are perpendicular to each other. Brewster's law is given by the formula: \[tan(\theta_p) = n\] Where \(\theta_p\) is the polarizing angle and \(n\) is the refractive index of the medium.

Using the given information, we know that: \[deviation = 22^{\circ}\] To calculate the refractive index, we need the formula for deviation: \[deviation = \theta_i + \theta_r - 90^{\circ}\] We also know that the polarizing angle is equal to angle of incidence when the deviation occurs: \[\theta_i = \theta_p\] Using Brewster's law, we have: \[tan(\theta_p) = n\] Now, we can calculate the refractive index: \[n = tan(\theta_p)\]

We can use Snell's law to find the angle of refraction (\(\theta_r\)): \[n = \frac{sin(\theta_i)}{sin(\theta_r)}\] We know that \(deviation = \theta_i + \theta_r - 90^{\circ}\) and \(\theta_i = \theta_p\), so: \[\theta_r = deviation + 90^{\circ} - \theta_p\] Now plug in the known values and calculate the angle of refraction: \[\theta_r = 22^{\circ} + 90^{\circ} - \theta_p\] Using Brewster's law, calculate \(\theta_p\): \[\theta_p = arctan(n)\] Finally, calculate the angle of refraction: \[\theta_r = 22^{\circ} + 90^{\circ} - arctan(n)\] The options given in the problem are: (A) \(44^{\circ}\) (B) \(34^{\circ}\) (C) \(22^{\circ}\) (D) \(11^{\circ}\) Calculate the angle of refraction (\(\theta_r\)) using the above formula and match with given options.