Question

Given that the reflectance and transmittance for a plane wave polarised perpendicular to the pl n by: ane of incidence are give I + αβ where sin θ sin θ cos θ cos θ and the angles of incidence are θί , and refraction, θ Assume that an incident wave (randomly polarized) from a medium with refractive index ni strikes a dielectric with refractive index n. Determine the degree of polarization of the reflected and transmitted waves when ni =1.0 and n2-1.5 and the angle of incidence θ,-30°. What is the qualitative effect on the reflected beam when θ= 56.31° ? '

Answer 1

For parallel polarization, the reflectance is:

$R_p = r_p^2 = \left( \frac{n_1cos\theta_2-n_2cos\theta_1}{n_1cos\theta_2+n_2cos\theta_1}\right )^2$

From Snell's law, $\theta_2 = sin^{-1}\frac{1sin30}{1.5} = 19.47\degree$

so, R_p = 0.0252

therefore, T_p = 1 - R_p = 0.9748

Degree of Polarization for reflected light is:

$P_{ref} = \left|\frac{R_s - R_p}{R_s+R_p}\right|\times 100\%$

similarly, Degree of Polarization for transmitted light is:

$P_{tra} = \left|\frac{T_s - T_p}{T_s+T_p}\right|\times 100\%$

substitute the values of R_s,R_p,T_s and T_p to get the degree of polarizations for both reflected and transmitted light.