Question

The optical activity of quartz, defined as the difference in the refractive indices for the two circular polarizations, is about 7×10 ⁻⁵, at the wavelength of a sodium lamp (λ=589 nm).

What thickness of this material would be required to convert x-polarized input light into ypolarized output light?

Answer 1

The thickness of the quartz required to convert x-polarized input light into y-polarized output light can be calculated using the equation d = Δϕ / (αλ), where Δϕ is the phase difference and α is the optical activity.

Step-by-step explanation:

The question asks for the thickness of quartz required to convert x-polarized input light into y-polarized output light. The optical activity of quartz is given as 7×10⁻⁵ at a wavelength of 589 nm. Optical activity is the ability of a substance to rotate the plane of polarization of light passing through it.

To convert x-polarized light to y-polarized light, we need to consider the phase difference between the two circular polarizations. The phase difference Δϕ is related to the thickness of the material d and the optical activity α by the equation Δϕ = αdλ, where λ is the wavelength of the light.

Given α = 7×10⁻⁵ and λ = 589 nm, we can rearrange the equation to solve for d: d = Δϕ / (αλ). Since we want to convert x-polarized input light into y-polarized output light, the phase difference Δϕ should be π/2 (90 degrees) or a multiple of π/2. Substitute Δϕ = π/2 into the equation to find the required thickness of the quartz.