Question

The angle of polarization of glass is 58° and that for water is 53°. The angle of polarization for glass in water is

• A. 55.5°
• B. tan-1x[tan-1(53°)tan-1(58°)]
• C. tan-1x[tan-1(58°)tan-1(53°)]
• D. tan-1(55.5°)

Answer 1

Answer: (C)

tan-1x[tan-1(58°)tan-1(53°)]

Answer 2

Explanation:
Given:The angle of polarization for glass, ig = 58°The angle of polarization for water, iw = 53°According to Brewster's law, the angle of polarization is related to the refractive index of the transparent medium:tan⁡(ip)=μg .....(i)and when the medium is water:tan⁡(iw)=μw .......(ii)Now, when the glass is in water, the relative refractive index of the system isμgμw=tan⁡(ig)tan⁡(iw)⇒μgμw=μgw=tan⁡(58∘)tan⁡(53∘)Let the angle of polarization be ip when a glass is in water. Then we gettan⁡(ip)=μgw=tan⁡(58∘)tan⁡(53∘)or, ip=tan−1⁡[tan⁡(58∘)tan⁡(53∘)]Hence, the correct option is (C).