When a wave hits an obstacle, it undergoes reflection, and when it passes through a different medium, it undergoes refraction. Diffraction, in which waves pass through a gap and spread out, also occurs.
Basic Knowledge
Law of reflection: angle of incidence = angle of reflection (the incident wave, reflected wave, and normal are all in the same plane)
・Reflection at a fixed end: The displacement reverses (crest → trough) at the fixed end and is reflected
・Reflection at a free end: The displacement remains unchanged (crest → crest) at the free end and is reflected
Law of refraction (Snell's law): sin θ₁ / sin θ₂ = v₁ / v₂ = n₂₁
・θ₁: angle of incidence, θ₂: angle of refraction
・v₁, v₂: wave speeds in media 1 and 2
・When entering a slower medium, the wave bends toward the normal (θ becomes smaller)
・When entering a faster medium, the wave bends away from the normal (θ becomes larger)
Diffraction: The phenomenon in which waves pass around the edge of an obstacle or through a gap and spread out. Diffraction occurs more readily when the gap is close to the wavelength.
Angles of incidence, reflection, and refraction（the angles formed by the normal and each ray）
Reflection at a fixed end（the phase reverses upon reflection. The displacement is inverted）
Reflection at a free end（the phase does not change upon reflection）
Refractive index（the ratio of the speed of light in a medium, c/v）
Snell's law（sin θ₁ / sin θ₂ = v₁ / v₂）
Diffraction（the phenomenon in which waves pass around the edge of an obstacle or through a gap）
Further Exploration (Background and Significance)
For the refraction of light, the refractive index n = c/v is used. When light enters glass (n≒1.5), its speed decreases to c/1.5, and it bends toward the normal. Dispersion, in which white light separates into seven colors in a prism, also occurs because of differences in refraction (the refractive index differs slightly depending on the color).
Total internal reflection: When light travels from a denser medium to a less dense medium (glass→air), all the light is reflected if the angle of incidence exceeds the critical angle. Optical fibers use this phenomenon to transmit light over long distances.
Diffraction of sound occurs commonly in daily life (you can hear a voice from beyond a wall), but because light has a short wavelength, diffraction is not noticeable with everyday obstacles. However, diffraction of light can be observed with narrow slits or diffraction gratings.
The wavelength of sound (about 1m) is similar to the width of a door gap (several tens of cm), so sound diffracts easily through the gap.
- Law of reflection: angle of incidence = angle of reflection
- Fixed end: phase reversal; free end: phase unchanged
- Snell's law: sin θ₁/sin θ₂ = v₁/v₂
- Slower medium → toward the normal
- Faster medium → away from the normal
- Total internal reflection = incidence exceeding the critical angle
- Diffraction: prominent when gap ≒ wavelength
Notes (Common Confusions)
① The angle of refraction is the angle formed with the normal. It is not the angle with the boundary surface. ② At a fixed end (wall), a crest is reflected as a trough; at a free end (the end of a rope), a crest is reflected as a crest. ③ According to Snell's law, θ becomes smaller when entering a slower medium (the wave bends toward the normal). This is often counterintuitive. ④ Total internal reflection occurs only from a slower medium to a faster medium (for example, glass→air). It does not occur in the opposite direction.
Practice
- For reflection at a fixed end, does a crest become a crest or a trough after reflection?
- When light enters glass (speed c/1.5) from air (speed c), is the angle of refraction larger or smaller than the angle of incidence?
- State the condition under which diffraction is likely to occur in terms of the relationship between the width of the gap and the wavelength.