Question

What is the reflectivity of a glass surface (n =1.5) in air (n = 1) at an 45° for (a) S-polarized light and (b) P-polarized light?

Answer 1

a)
`R_s = 0.092`

b)
`R_p = 0.085`

Step-by-step explanation:

given,

n =1.5 for glass surface

n = 1 for air

incidence angle = 45°

using Fresnel equation of reflectivity of S and P polarized light

`R_s=\left | (n_1cos\theta_i-n_2cos\theta_t)/(n_1cos\theta_i+n_2cos\theta_t) \right |^2\\R_p=\left | (n_1cos\theta_t-n_2cos\theta_i)/(n_1cos\theta_t+n_2cos\theta_i) \right |^2`

using snell's law to calculate θ t

`sin \theta_t = (n_1sin\theta_i)/(n_2)=(sin45^0)/(1.5)=(√(2))/(3)`

`cos \theta_t =√(1-sin^2\theta_t) = \frac{sqrt{7}}{3}`

a)
`R_s=\left | ((1)/(√(2))-(1.5√(7))/(3))/((1)/(√(2))+(1.5√(7))/(3)) \right |^2`

`R_s = 0.092`

b)
`R_p=\left | ((√(7))/(3)-(1.5)/(√(2)))/((√(7))/(3)+(1.5)/(√(2))) \right |^2`

`R_p = 0.085`