Geometric optics and wave optics (interference, diffraction)
Geometric and wave optics
This domain tests reflection, refraction, Snell's law, total internal reflection, lenses and mirrors, and interference and diffraction. You should be able to decide whether an image is real or virtual and to calculate fringe spacing or a diffraction angle.
Core rules
- Refraction: n1 sinθ1=n2 sinθ2, with angles measured from the normal. Light bends toward the normal when entering a denser medium. Frequency is unchanged; wavelength becomes λ/n.
- Critical angle: sinθc=n2/n1 for n1>n2. Beyond θc, total internal reflection occurs.
- Lenses and mirrors: 1/f=1/d_o+1/d_i and m=−d_i/d_o. Real images can be projected; virtual images cannot.
- Double slit: bright fringes at d sinθ=mλ; for small angles, spacing Δy=λL/d.
- Diffraction grating: maxima at d sinθ=mλ, with sharper peaks than a double slit.
- Single slit: minima at a sinθ=mλ for m=±1,±2,…, giving a central maximum twice as wide as the side maxima.
Worked example
In a double-slit experiment, λ=600 nm, slit separation d=0.20 mm and screen distance L=2.0 m. The fringe spacing is Δy=λL/d=(600×10⁻⁹)(2.0)/(0.20×10⁻³)=6.0×10⁻³ m, or 6.0 mm. The third bright fringe is 18 mm from the centre. If the apparatus is immersed in water with n=1.33, the wavelength in water is 451 nm and the spacing falls to about 4.5 mm, because frequency stays the same.
Traps
Measuring angles from the surface instead of the normal; using the vacuum wavelength inside a medium; applying a mirror sign convention to a lens without adjusting signs; confusing double-slit maxima with single-slit minima; assuming a virtual image is always smaller; forgetting that a grating's spacing d is the distance between adjacent slits.