State the four conditions for obtaining well defined and steady interference pattern.Light incident at angle 52.5° on a bucket filled with water be completely polarised after reflection. Calculate the refractive index of the water.

Answer: Refractive index of water \(n = \tan52.5^\circ \approx 1.303\).

(i) Conditions for a well-defined and steady interference pattern:

1. The two sources must be coherent, i.e. they must maintain a constant phase difference (in practice, they are derived from a single source).
2. The two sources should emit light of the same wavelength (monochromatic light of the same frequency).
3. The amplitudes (intensities) of the two interfering waves should be equal or nearly equal, so that dark fringes are perfectly dark and contrast is good.
4. The two sources should be narrow and very close to each other, and the screen should be at a large distance from them, so that the fringes are wide enough to be seen distinctly.

(Also, the waves should travel along nearly the same direction and, if polarized, be in the same state of polarization.)

(ii) Numerical: Reflected light is completely polarized when it is incident at the polarizing (Brewster) angle \(\theta_B\). By Brewster’s law \(n = \tan\theta_B\).