Fix the mistake: Light Waves

Properties of Light・Reflection・Refraction

Light is an electromagnetic wave and a transverse wave. Let us review the laws of reflection and refraction, and learn about total internal reflection and the critical angle from Snell’s law.

Basic Knowledge

Light is an electromagnetic wave, and its speed in a vacuum is c = 3.0×10⁸ m/s. Because it is a transverse wave, it can be polarized.
Law of reflection: angle of incidence = angle of reflection (the angles of incidence and reflection are the angles between the normal and the light rays)
Snell’s law (law of refraction): n₁ sin θ₁ = n₂ sin θ₂
（n₁, n₂: refractive indices of the respective media，θ₁: angle of incidence，θ₂: angle of refraction）
Refractive index n: speed in a vacuum / speed in a medium n = c/v（n ≥ 1）
Total internal reflection: When n₁ > n₂ (light travels from an optically denser medium to a rarer medium), if the angle of incidence exceeds the critical angle θc, there is no refracted ray and the light is completely reflected.
sin θc = n₂/n₁

Important Terms
Refractive index n（n = c/v. An indicator of how difficult it is for light to travel through a medium）
Snell’s law（n₁ sin θ₁ = n₂ sin θ₂. The change in the direction of light at a boundary）
Total internal reflection（The phenomenon in which light is confined within a medium when the critical angle is exceeded）
Critical angle θc（sin θc = n₂/n₁. The angle at which total internal reflection begins）
Optical fiber（A communication medium that uses total internal reflection to transmit light over long distances）

Further Study (Background・Significance)

Optical fibers are a representative engineering application of total internal reflection. Light is transmitted while repeatedly undergoing total internal reflection at the boundary between the core and cladding, enabling lower-loss and faster communication than metal cables.
The critical angle of diamond is very small, ~24° (its refractive index is large, ~2.42), and its brilliance increases because total internal reflection occurs at many faces of a multi-faceted cut.
The “window of the sky (fish-eye)” seen from underwater (the phenomenon in which, when looking at the surface from underwater, only a circular window within the critical angle can be seen) is also a result of total internal reflection.

Key Points
  • n = c/v（refractive index = speed in a vacuum / speed in a medium）
  • Snell’s law: n₁ sin θ₁ = n₂ sin θ₂
  • From denser to rarer, sin θ increases, so total internal reflection can occur
  • sin θc = n₂/n₁（when n₁ > n₂）
  • Applications of total internal reflection: optical fibers and the brilliance of diamonds

Points to Note (Easily Confused)

① Total internal reflection occurs only in the direction from a denser to a rarer medium (n₁ > n₂). It is impossible from a rarer to a denser medium. ② The formula for θc is sin θc = nrarer/ndenser (confirm that it is < 1). ③ The angles in Snell’s law are “angles measured from the normal” (not from the boundary). ④ n₁ sin θ₁ = n₂ sin θ₂ results from the continuity condition at a boundary and is a different equation from the law of reflection.

Practice

  1. Find the speed of light in glass with a refractive index of 1.5 (c = 3.0×10⁸ m/s).
  2. Find the angle of refraction of light entering glass (n₂ = 1.5) from air (n₁ = 1.0) at an angle of 30°.
  3. Find the critical angle θc for total internal reflection from glass (n = 1.5) to air (only the value of sin is required).

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