Soru

Passage

In his 1690 treatise Traité de la lumière, the Dutch polymath Christiaan Huygens formulated the first comprehensive wave theory of light, challenging the prevailing mechanistic view that light consisted of streams of discrete corpuscles. While Huygens successfully derived the laws of reflection and standard refraction by modeling light as propagating longitudinal wave-fronts composed of innumerable secondary spherical wavelets, his theory confronted an intricate empirical obstacle: the phenomenon of double refraction in Iceland spar (calcite crystals), first described by Erasmus Bartholin in 1669. When an incident ray of light enters a rhomb of Iceland spar along any direction other than its optic axis, it bifurcates into two distinct refracted rays—the "ordinary ray," which strictly obeys Snell’s law of constant refractive indices, and the "extraordinary ray," which deviates from standard trigonometric ratios and bends at anomalous angles.

Corpuscular theorists, most notably Isaac Newton and his acolytes, argued that this bifurcation exposed fatal inadequacies in wave-based models. Newton contended that because longitudinal waves in fluid media should theoretically disperse uniformly in every direction without directional preference, a wave-front could not inherently separate into two divergent paths exhibiting distinct geometric behaviors. In response to this skepticism, Huygens proposed a sophisticated geometric modification to his principle of secondary wave propagation. Rather than assuming that light waves always expand as isotropic spheres, Huygens posited that the structural composition of certain anisotropic crystals alters the velocity of wave propagation depending on the direction of travel through the crystalline lattice.

Specifically, Huygens demonstrated that inside calcite, the ordinary ray propagates via secondary wavelets that remain perfectly spherical, expanding at uniform speed throughout the medium. Conversely, the extraordinary ray propagates via secondary wavelets that take the form of flattened ellipsoidal (oblate spheroidal) shells. Huygens hypothesized that this directional variance in velocity arises because the constituent particles of calcite are themselves elliptical or packed with asymmetric interstitial spacing, causing secondary disturbances to encounter varying mechanical resistance along different axes. By constructing the envelope tangent to these overlapping ellipsoidal wavelets, Huygens was able to calculate the precise path of the extraordinary ray with astonishing mathematical precision.

Nonetheless, Huygens’s mechanical explanation remained incomplete. He could not explain why rotating a second calcite crystal placed in the path of the emerging rays caused alternating variations in their relative intensities—a property later recognized as transverse polarization. Because Huygens conceived of light waves strictly as longitudinal pressure pulses within an ethereal medium, analogous to acoustic waves in air, he lacked the theoretical concept of transverse oscillations perpendicular to the ray's trajectory. Despite this theoretical limitation, Huygens’s geometric construction of ellipsoidal wavelets stood as a foundational milestone in physical optics, demonstrating that complex optical deviations could be rigorously explained through non-spherical wave propagation.

According to the passage, Huygens hypothesized that directional differences in the velocity of light propagation inside calcite are caused by which of the following?