Wavefronts, rays and boundary behaviour

• Wavefronts join points that are in the same phase.

• Rays show the direction of energy transfer and are perpendicular to wavefronts.

• At a boundary, waves can undergo reflection, refraction and transmission.

• In reflection, the wave remains in the original medium and the angle of incidence = angle of reflection.

• In refraction, the wave enters a new medium and its speed changes.

• When a wave changes medium, frequency stays constant but wavelength changes because $v=f\lambda$.

• If a wave slows down, it bends towards the normal.

• If a wave speeds up, it bends away from the normal.

• In wavefront-ray diagrams, bending is explained by one side of the wavefront changing speed before the other.

This diagram shows refraction at a boundary with the normal, incident angle, refracted angle and wave speeds labeled. It is useful for linking the geometry of the ray to Snell’s law. Use it to see why changing speed causes bending at the boundary. Source

Snell’s law, refractive index and total internal reflection

• Snell’s law: $\dfrac{n_1}{n_2}=\dfrac{\sin \theta_2}{\sin \theta_1}=\dfrac{v_2}{v_1}$.

• $\theta$ is always measured between the ray and the normal.

• A larger refractive index means lower wave speed in that medium.

• Rearranged form often used: $n_1\sin\theta_1=n_2\sin\theta_2$.

• Critical angle occurs when the refracted ray travels along the boundary, so angle of refraction is $90^\circ$.

• Total internal reflection (TIR) occurs when light goes from higher $n$ to lower $n$ and the angle of incidence is greater than the critical angle.

• At the critical angle, $\sin c = \dfrac{n_2}{n_1}$ for light travelling from medium 1 to 2 where $n_1>n_2$.

• TIR gives no refracted ray; all the light is reflected internally.

• Common exam trap: TIR cannot happen when light travels from lower $n$ to higher $n$.

This image shows the critical angle and what happens when the angle of incidence becomes large enough for total internal reflection. It helps distinguish ordinary refraction, the critical case, and complete internal reflection. Use it when explaining why TIR only occurs from more optically dense to less optically dense medium. Source

Diffraction and wavefront-ray diagrams

• Diffraction is the spreading out of waves around a body or after passing through an aperture.

• Diffraction is most noticeable when the gap size or obstacle size is comparable to the wavelength.

• Large wavelength or small aperture gives more diffraction.

• If the aperture is much larger than the wavelength, diffraction is less significant.

• Wavefront diagrams for diffraction show the wave emerging from the gap as curved wavefronts.

• Diffraction does not require a change of medium.

• At normal incidence, the central maximum is centred on the original direction of travel.

Superposition and interference

• Superposition means the resultant displacement at a point is the sum of the individual displacements.

• This applies to both waves and wave pulses.

• When waves meet, they pass through each other and continue, but the overlap can produce interference.

• Constructive interference gives a maximum amplitude.

• Condition for constructive interference: path difference $= n\lambda$.

• Destructive interference gives a minimum amplitude.

• Condition for destructive interference: path difference $= \left(n+\dfrac{1}{2}\right)\lambda$.

• Double-source interference requires coherent sources.

• Coherent sources produce waves of the same frequency with a constant phase difference.

• Exam tip: always decide whether