Light & Sound Waves

• Mechanism of Reflection: Reflection occurs when a wave reaches a boundary between two different media and is sent back into its original medium rather than passing through. An everyday application of this is an echo, which is specifically the reflection of sound waves off a hard surface.

• The Law of Reflection: This fundamental principle states that the angle of incidence ($i$) is exactly equal to the angle of reflection ($r$). These angles are not measured from the surface itself, but from the normal line, which is an imaginary perpendicular line drawn at 90° to the boundary.

• Ray Diagrams: In optics, we represent waves as rays with arrows indicating the path of travel. The incident ray points toward the boundary, while the reflected ray points away, ensuring the geometry satisfies the law of reflection relative to the normal.

• Concept of Refraction: Refraction is the change in direction of a wave as it passes from one transparent medium to another of different optical density. This bending occurs because the speed of the wave changes as it enters a material where it travels more slowly or more quickly.

• Directional Rules: When light moves from a less dense medium (like air) to a more dense medium (like glass), it slows down and bends towards the normal. Conversely, moving from a denser to a less dense medium causes it to speed up and bend away from the normal.

• Mathematical Foundation: Snell's Law quantifies this relationship using the refractive index ($n$). The formula is given by:

$n = \frac{\sin i}{\sin r}$

• Invariance of Frequency: It is vital to note that during refraction, only the speed and wavelength change; the frequency of the wave remains constant. This is why light does not change color when it refracts, as color is determined by frequency.

• The Critical Angle: As the angle of incidence increases when moving from a dense to a less dense medium, the angle of refraction also increases. The critical angle ($c$) is reached when the refracted ray travels exactly 90° to the normal, effectively moving along the boundary.

• Conditions for TIR: Total Internal Reflection occurs only when two conditions are met: the light must be traveling from a more dense to a less dense medium, and the angle of incidence must be greater than the critical angle ($i > c$).

• Mathematical Relationship: The critical angle is inversely related to the refractive index of the material. This relationship is expressed by the formula:

$\sin c = \frac{1}{n}$

• Applications: TIR is the principle behind optical fibres, where light reflects repeatedly off the inner walls to transmit data over long distances. It is also used in prisms for devices like periscopes and binoculars.

• Transverse vs. Longitudinal: It is crucial to distinguish wave types. Transverse waves (light) oscillate perpendicular to travel, while longitudinal waves (sound) oscillate parallel. This determines whether they require a medium and how they are visually represented.

• Critical Angle vs. Refraction: Refraction occurs for all angles smaller than the critical angle. Once the critical angle is exceeded, refraction ceases entirely and is replaced by Total Internal Reflection.

• Always Draw the Normal: Every ray diagram must start with a dashed normal line at 90° to the boundary. Exams frequently penalize students who measure angles from the surface instead of the normal.

• Label Ray Direction: Use arrows on your rays to show where the light is coming from and where it is going. A ray without an arrow is just a line and may not receive marks.

• The Calculator Check: When using Snell's Law or calculating the critical angle, ensure your calculator is in Degree mode. Also, remember that refractive index $n$ must always be greater than 1 for materials denser than a vacuum.

• Sanity Check for Bending: Use the mnemonic 'TAG' (Towards Air to Glass) to remember that light bends towards the normal when slowing down, and 'Leaves Away' when it speeds up leaving a block.