Waves, Sound and Optics
Wave properties and superposition
For any wave, v = fλ. Transverse waves oscillate perpendicular to energy transfer; longitudinal waves oscillate parallel to it. Sound is longitudinal and needs a medium. Superposition adds displacements. Stationary waves form when two waves of the same frequency travel in opposite directions; nodes are points of zero amplitude and antinodes are points of maximum amplitude.
Refraction and lenses
Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, with angles measured from the normal. Frequency is unchanged on refraction; speed and wavelength change. Total internal reflection occurs only from a denser to a less dense medium when the angle exceeds the critical angle, sin c = n₂/n₁. A converging lens forms real images when the object is beyond the focal point; a diverging lens forms virtual images.
Worked example
Light travels from air into glass of refractive index 1.50 at an angle of incidence of 40°. Find the angle of refraction and the critical angle. sin r = sin 40° ÷ 1.50 = 0.4285, so r = 25.4°. The critical angle satisfies sin c = 1/1.50, so c = 41.8°. The ray bends towards the normal because glass is optically denser than air.
Traps
Measuring angles from the surface instead of the normal; thinking frequency changes on refraction; applying total internal reflection from less dense to denser; mixing path-difference conditions for constructive and destructive interference; forgetting that a virtual image cannot be projected onto a screen.