Waves and Optics
The Waves and Optics domain tests wave properties, sound, standing waves, reflection and refraction, lenses and mirrors, and interference. Expect questions that ask what changes and what stays the same when a wave crosses a boundary.
Wave fundamentals
v = fλ, and T = 1/f. The medium sets the speed; the source sets the frequency. When a wave enters a new medium, frequency is unchanged, while speed and wavelength change together. Standing waves have nodes (zero displacement) and antinodes (maximum). On a string fixed at both ends, f_n = nv/(2L).
Sound
Sound is longitudinal and needs a medium. The Doppler effect raises observed frequency when source and observer approach and lowers it when they separate. Loudness in decibels is logarithmic.
Reflection, refraction, lenses
Angle of incidence equals angle of reflection. Snell's law: n₁ sinθ₁ = n₂ sinθ₂. Light bends toward the normal when entering a denser medium (larger n). Total internal reflection occurs only from denser to less dense, beyond sinθ_c = n₂/n₁. Thin-lens and mirror equation: 1/f = 1/d_o + 1/d_i, with magnification m = −d_i/d_o. Real images have positive d_i for mirrors and form on the opposite side of a lens; virtual images have negative d_i.
Interference
For a double slit, constructive interference occurs when d sinθ = mλ. A path difference of a whole number of wavelengths gives constructive interference; a half-integer gives destructive.
Worked example
Light in air (n = 1.00) strikes glass (n = 1.50) at 40°. Find the refracted angle. sinθ₂ = (n₁ sinθ₁)/n₂ = (1.00 × sin40°)/1.50 = 0.643/1.50 = 0.429, so θ₂ ≈ 25°. The ray bends toward the normal, as expected when entering the denser medium.
Traps
- Calculator in radians when the problem is in degrees.
- Changing frequency at a boundary.
- Using n = 1.00 for the second medium in Snell's law.
- Dropping the negative sign on magnification.
- Assuming total internal reflection can happen entering a denser medium.