Plane polarized light is incident on a piece of quartz cut parallel to the axis. Find the least
thickness for which the ordinary and the extraordinary rays combine to form plane
polarized light. Given, μe = 1.5533, μo = 1.5442 and λ = 500 nm.?

Question

Answer

Introduction:

When plane polarized light is incident on a piece of quartz, it splits into two rays: one ordinary and the other extraordinary. The least thickness of the quartz through which both rays combine to form plane polarized light is called the thickness of the quartz plate.

Given:

μe = 1.5533

μo = 1.5442

λ = 500 nm

Formula:

For ordinary ray: no = 1.5442

For extraordinary ray: ne = 1.5533

Phase difference between the two rays: δ = (2π/λ) * d * (ne - no)

For constructive interference: δ = 2πn (where n is an integer)

Least thickness: dmin = (λ/(2(ne-no))) * n

Calculation:

ne - no = 1.5533 - 1.5442 = 0.0091

For n = 1, dmin = (500 * 10^-9)/(2 * 0.0091) = 27.47 μm

Therefore, the least thickness for which the ordinary and extraordinary rays combine to form plane polarized light is 27.47 μm.

Explanation:

When plane polarized light is passed through a quartz crystal, it splits into two rays: one ordinary and the other extraordinary. The ordinary ray obeys the laws of refraction and reflection like any other wave, while the extraordinary ray does not. The two rays have different refractive indices, which causes them to travel at different speeds. When the two rays recombine, they can either interfere constructively or destructively, depending on the thickness of the quartz. When the thickness of the quartz is such that the two rays interfere constructively, they combine to form plane polarized light. The least thickness at which this occurs is called the thickness of the quartz plate. The formula for calculating the thickness of the quartz plate involves the refractive indices of the two rays, the wavelength of the incident light, and the phase difference between the two rays. By using this formula and the given values of the refractive indices and wavelength, we can calculate the thickness of the quartz plate.

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