Consider a ray of 700 nm unpolarized light. Assume it is incident on a piece of
ID: 1997743 • Letter: C
Question
Consider a ray of 700 nm unpolarized light. Assume it is incident on a piece of glass with n=1.42. At what angle is the reflected light polarized? Draw the corresponding detailed diagram. Assume it is incident instead on a piece of calcite crystal that is cut such that the optic axis is parallel to the front face and perpendicular to the plane of incidence. If the angle of incidence is 45 degrees, what is the angular separation between the ordinary and extraordinary rays within the calcite? Draw the corresponding detailed diagram.Explanation / Answer
(a). Index of refraction of glass n= 1.42
The reflected light is polarized when the incident light is equal to angle of polarization(P)
So, angle of incidence = angle of polarization
= tan -1 (n)
= tan -1 (1.42)
= 54.84 o
(b).Index of refraction of ordinary ray in calcite crystal, no = 1.658
Index of refraction of extra ordinary ray in calcite crystal, ne = 1.486
Angle of incidence i = 45 o
Apply Snell's law for ordinary ray,
sin i / sin r = no /n '
Where n' = index of refraction of air = 1
sin 45 / sin r = 1.658
sin r = sin 45 / 1.658
= 0.4264
r = sin -1 (0.4264)
= 25.24 o
Apply Snell's law for extra ordinary ray,
sin i / sin r ' = ne /n '
Where n' = index of refraction of air = 1
sin 45 / sin r ' = 1.486
sin r ' = sin 45 / 1.486
= 0.4758
r ' = sin -1 (0.4758)
= 28.41 o
The angular separation between the ordinary and extraordinary rays in the calcite = r ' - r
= 28.41 o - 25.24 o
= 3.17 o