What will be the velocity of an extraordinary ray in a given crystal with a refractive index of the extraordinary ray is 1.49 and the speed of light in a vacuum is 3× 10⁸ m/s. 

Concept:

Double refraction is an optical property in which a single ray of unpolarized light entering an anisotropic medium is split into two rays, each traveling in a different direction.

• Refraction occurs when a beam of light passes from one material into another material. At the surface of the two materials, the path of the beam changes its direction.
• The refracted beam acquires some degree of polarization. Most often, the polarization occurs in a plane perpendicular to the surface.
• Light passing through a calcite crystal is split into two rays. This process is called double refraction. The two rays of light are each plane-polarized by the calcite such that the planes of polarization are mutually perpendicular.
• Double refraction, also called birefringence, an optical property in which a single ray of unpolarized light entering an anisotropic medium is split into two rays, each traveling in a different direction.
• One ray (called the extraordinary ray) is bent, or refracted, at an angle as it travels through the medium;
• The other ray (called the ordinary ray) passes through the medium unchanged.

• Double refraction can be observed by comparing two materials, glass and calcite.

Snell's law:

• Snell's law or the law of refraction states that the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is constant for a light of given wavelength traveling in a given pair of media.

           \(\frac{sin\; i}{sin\; r}=constant = μ= \frac{v_1}{v_2}\)

Where μ  = refractive index of the second medium with respect to the first medium.

Calculation:

Given that,

μ_e = 1.49

c = 3× 108 m/s

Now according to snell's law 

\(μ= \frac{c}{v_e}\Rightarrow v_e=\frac{c}{\mu_e}=2.01\times 10^8 m/s\)

Additional Information

Some of the differences between o-ray and e-ray are as shown below