Wave Phenomena

Reflection occurs when a wave hits a boundary and returns to the original medium, following the law where the angle of incidence ($\theta_i$) equals the angle of reflection ($\theta_r$).

Refraction is the change in direction of a wave as it passes from one medium to another due to a change in its propagation speed.

The refractive index ($n$) of a material is a dimensionless number representing the ratio of the speed of light in a vacuum ($c$) to the speed in the material ($v$): $n = \frac{c}{v}$

Snell's Law describes the relationship between the angles and refractive indices of two media: $n_1 \sin \theta_1 = n_2 \sin \theta_2$

During refraction, the frequency of the wave remains constant, while the speed and wavelength change proportionally.

Diffraction is the spreading out of waves as they pass through an aperture or around an edge. This effect is most significant when the wavelength is approximately equal to the gap size ($b$).

If the gap is much larger than the wavelength ($b \gg \lambda$), diffraction is negligible; if the gap is smaller or equal ($b \le \lambda$), the wave spreads significantly into the 'shadow' region.

Polarization is a phenomenon exclusive to transverse waves, where the oscillations are restricted to a single plane perpendicular to the direction of energy transfer.

Longitudinal waves (like sound) cannot be polarized because their oscillations are always parallel to the direction of travel.

Normal Line: Always draw the normal line perpendicular to the boundary before measuring angles. Students often mistakenly measure angles from the surface instead of the normal.

Refractive Index Logic: Remember that a higher refractive index ($n$) means a slower speed ($v$). Light always bends towards the normal when entering a more optically dense medium (higher $n$).

Diffraction Conditions: If an exam question asks why diffraction is not visible, check the ratio of wavelength to gap size. If $\lambda \ll b$, the wave behaves like a ray and does not spread.

Frequency Invariance: In refraction problems, never change the frequency. If the speed doubles, the wavelength must also double to keep $f$ constant.

The 'Sound Polarization' Trap: A common error is assuming sound can be polarized. Sound is longitudinal; it has no 'side-to-side' oscillation to restrict.

Energy in Diffraction: While the wavelength and frequency remain constant during diffraction, the amplitude (and thus intensity) decreases as the wave energy spreads over a larger area.

Index of Refraction Limits: The value of $n$ is always $\ge 1$ because light cannot travel faster than $c$ in any medium.