Refraction

The phenomenon in which the direction of travel changes when waves such as light, radio waves, and sound waves are incident on the interface between two media with different refractive indices and travel into the second medium. As shown in the figure , the angle _θ1 between the normal to the interface HOH' and the direction of travel of the incident wave AO is called the angle of incidence, and the angle _θ2 between the normal to the interface HOH _' and the direction of travel of the refracted wave OA' is called _the angle of refraction, and Snell's law (law of refraction) _sinθ1 / _sinθ2 ＝ n2 / _n1 ( n2 _{and n1} are the refractive indices of the second and first media , respectively) holds true between θ1 _and θ2 .

Newton explained the phenomenon of refraction using a model that considers light as a particle. That is, when n ₂ > n ₁ , | v ₂ | > | v ₁ | (| v ₂ | and | v ₁ | are the magnitudes of the light's propagation speed in the second and first media, respectively), and the magnitudes of the partial velocities of the velocity vectors v ₁ and v ₂ within the boundary surface are equal, that is, the relationship sinθ ₁ /sinθ ₂ = | v ₂ |/| v ₁ | holds. This treatment was later experimentally proven to be incorrect, as it was shown that the propagation speed of light is slower when it travels through a medium with a higher refractive index. Huygens considered light to be a wave, and clearly explained the reflection and refraction of light using the concept of secondary waves. It is now known that Snell's law applies not only to waves such as light and sound waves, but also to the refraction of particles such as electrons.In this case, instead of the velocity vectors v1 and v2 mentioned above, quantities _k1 and _k2 called wave vectors _, which are inversely proportional to the velocity and therefore proportional to the refractive index _, are used and are commonly expressed in _the form _sinθ1 / _sinθ2 ＝| k2 |/| k1 | _.

Even if the boundary surface is not flat, refraction by a spherical surface such as a lens can be handled if Snell's law holds true at each point where the wave is incident. The refractive index of a material usually decreases with increasing wavelength, so when white light is incident on a prism, the light that is refracted through two boundaries and leaves the prism changes direction more for shorter wavelength components, and the white light is dispersed and split into a spectrum. If we reverse the direction of travel of the wave in the diagram and consider the case where it propagates from a medium with a high refractive index to a medium with a low refractive index, Snell's law dictates that the angle of refraction (θ ₁ in this case) will be greater than the angle of incidence (θ ₂ ).

If the angle of incidence is gradually increased, the angle of refraction becomes 90 degrees, and at angles of incidence greater than this, no refracted waves exist, and the incident wave is reflected 100% at the boundary surface. This phenomenon is called total reflection, and the angle of incidence at which the angle of refraction is 90 degrees is called the critical angle for total reflection. Unlike sound waves, electromagnetic waves such as radio waves, light, and X-rays are transverse waves whose vibration direction is perpendicular to the direction of propagation. Therefore, the waves that vibrate within the plane of the paper in the figure and those that vibrate perpendicular to the plane of the paper behave differently, and there is a difference in the amplitude of the refracted wave. When natural light is incident, the refracted wave is partially polarized. Up until now, we have considered refraction at the boundary surface between two homogeneous media, but when a wave propagates through a medium in which the refractive index changes continuously, the direction of the wave's propagation also changes continuously.

Furthermore, when light enters a medium such as a crystal that has anisotropic refractive index, the refracted light generally splits into two components traveling in different directions, a phenomenon known as birefringence. When light enters a medium that involves absorption, Snell's law is formally satisfied if the refractive index is expressed as a complex number that takes absorption into account, and is called the complex refractive index. However, in this case, _θ2 is also a complex number, and it no longer has the meaning of the refraction angle.

[Tanaka Shunichi]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

屈折率の異なる二つの媒質の境界面に光、電波、音波などの波動が入射して第2媒質に進むとき、進行方向が変わる現象。図に示すように、境界面の法線HOH′と入射波の進行方向AOとのなす角θ₁を入射角、また屈折波の進行方向OA′とのなす角θ₂を屈折角とよび、θ₁とθ₂との間にはスネルの法則（屈折の法則）sinθ₁/sinθ₂＝n₂/n₁（n₂、n₁はそれぞれ第2、第1媒質の屈折率）が成立する。

　ニュートンは光を粒子と考えるモデルで屈折現象の説明を行った。すなわちn₂＞n₁のとき、|v₂|＞|v₁|（|v₂|、|v₁|はそれぞれ第2、第1媒質中の光の伝播(でんぱ)速度の大きさ）で、速度ベクトルv₁、v₂の境界面内の分速度の大きさが等しくなる、すなわちsinθ₁/sinθ₂＝|v₂|/|v₁|の関係が成立するとした。この取扱いは、のちに、屈折率の高い媒質を伝わる光ほどその伝播速度が小さいことが実験的に確かめられ、誤りが明白になった。ホイヘンスは光を波動と考え、二次波の概念を使って光の反射、屈折を明確に説明した。なお現在では、光、音波などの波動のほかに電子のような粒子の屈折に対してもスネルの法則が成立することが知られており、この場合、先に述べた速度ベクトルv₁、v₂のかわりに速度に逆比例、したがって屈折率に比例する波数ベクトルとよばれる量k₁、k₂を用いsinθ₁/sinθ₂＝|k₂|/|k₁|の形で共通的に表示される。

　境界面が平面でない場合も、波動が入射する各点でスネルの法則が成立するとすれば、レンズなどの球面による屈折を取り扱うことができる。物質の屈折率は普通、波長の増大とともに減少するので、プリズムに白色光を入射すると、境界面二つを屈折してプリズム外へ出る光は波長の短い成分ほど大きく向きを変え、白色光は分散されてスペクトルに分かれる。図で波動の進行方向を逆にとり、屈折率の高い媒質から低い媒質へ伝播する場合を考えると、スネルの法則によって屈折角（この場合θ₁）のほうが入射角（θ₂）より大きくなる。

　ここで入射角をしだいに大きくしていくと屈折角は90度になり、さらにこれ以上の入射角では屈折波が存在せず、入射波は境界面で100％反射されるようになる。この現象は全反射とよばれ、屈折角が90度のときの入射角を全反射の臨界角という。電波、光、X線などの電磁波は、音波と異なり波の振動方向が伝播方向に垂直な横波である。そのため、図の紙面内で振動する波と紙面に垂直方向に振動する波とではようすが異なり、屈折波の振幅の大きさに相違が生じる。自然光を入射した場合、屈折波は部分的に偏光する。これまでは均質な媒質二つの境界面での屈折を考えたが、屈折率が連続的に変化するような媒質中を波動が伝播する場合は、波動の進行方向も連続的に変化することになる。

　また屈折率に異方性をもつ結晶のような媒質に光が入射する場合は、一般に屈折光は進行方向が異なる二つの成分に分かれ、複屈折とよばれる現象を示す。吸収を伴う媒質に光が入射する場合は、屈折率として、吸収も考慮に入れた複素数で表される複素屈折率とよばれる量を用いれば、形式的にはスネルの法則がそのまま満足される。しかしこの場合は、θ₂も複素数になり、もはや屈折角の意味はもたない。

［田中俊一］

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