The Huygens theory of double refraction explains the phenomenon of birefringence, where light is split into two rays when passing through certain materials, such as crystals. When the optic axis is parallel to the refracting surface and lies in the plane of incidence, the Huygens theory predicts specific behaviors for normal and oblique incidence.

Normal Incidence

When light is incident normally on a birefringent crystal with the optic axis parallel to the surface, the Huygens theory predicts that the incident ray will split into two rays: an ordinary ray and an extraordinary ray. The ordinary ray will behave as if the crystal is isotropic, meaning it will not experience double refraction and will travel through the crystal at a constant speed. The extraordinary ray, on the other hand, will experience double refraction and will split into two rays: a fast ray and a slow ray. The fast ray will travel faster than the ordinary ray, while the slow ray will travel slower.

Oblique Incidence

When light is incident obliquely on a birefringent crystal with the optic axis parallel to the surface, the Huygens theory predicts that the ordinary and extraordinary rays will behave differently. The ordinary ray will still behave as if the crystal is isotropic and will follow the laws of reflection and refraction as if it were passing through a single medium. The extraordinary ray, however, will split into two rays with different refractive indices and will follow different paths through the crystal.

Conclusion

In conclusion, the Huygens theory of double refraction explains the behavior of light passing through birefringent crystals with the optic axis parallel to the surface. When light is incident normally, the ordinary and extraordinary rays will behave differently, with the extraordinary ray splitting into two rays. When light is incident obliquely, the ordinary and extraordinary rays will still behave differently, but the extraordinary ray will split into two rays with different refractive indices.