Light & Sound Waves

The Law of Reflection: When a wave strikes a boundary and remains in its original medium, the angle of incidence ($i$) is always equal to the angle of reflection ($r$). Both angles are measured from the normal, an imaginary line perpendicular to the surface at the point of impact.

Refraction and Optical Density: Refraction is the change in direction of a wave as it crosses a boundary between two media of different densities. This occurs because the wave's speed changes; light slows down in denser materials (like glass) and speeds up in less dense materials (like air).

Wave Invariants: During refraction, the frequency of the wave remains constant. Because the speed ($v$) changes, the wavelength ($\lambda$) must also change to satisfy the wave equation $v = f\lambda$.

Snell's Law: The relationship between the angles and the refractive index ($n$) is given by the formula $n = \frac{\sin i}{\sin r}$. This allows for the calculation of how much a ray will bend when entering a specific material.

Calculating Refractive Index: The refractive index can also be defined as the ratio of the speed of light in a vacuum ($c$) to the speed of light in the material ($v$): $n = \frac{c}{v}$. Since $c$ is the maximum possible speed, $n$ is always greater than or equal to 1.

Ray Diagram Construction: To accurately predict wave paths, always draw the normal first. Use a ruler for straight lines and arrows to indicate the direction of energy flow. When moving from a less dense to a more dense medium, the ray bends towards the normal; when moving to a less dense medium, it bends away.

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 ($c$).

The Critical Angle: This is the specific angle of incidence that results in an angle of refraction of exactly $90^{\circ}$, causing the light to travel along the boundary. It is calculated using the formula $\sin c = \frac{1}{n}$.

Applications: TIR is the operating principle behind optical fibers, where light is trapped inside a glass core by constant internal reflection. This technology is vital for high-speed telecommunications and medical endoscopes.

The Normal is Key: Always measure angles $i$ and $r$ from the normal line, never from the surface of the material. This is the most common source of calculation errors in exams.

Sanity Checks: If light enters a denser medium (like glass), the angle of refraction $r$ must be smaller than the angle of incidence $i$. If your calculation shows $r > i$ in this scenario, you have likely inverted the Snell's Law fraction.

Calculator Settings: Ensure your calculator is in Degree mode rather than Radians when performing trigonometric functions for these problems.

Units: Remember that the refractive index ($n$) is a ratio of two identical units (or sines of angles), meaning it is a dimensionless quantity and should not have units.