diffraction grating
Summary
A diffraction grating is a surface with many equally spaced parallel slits or lines that produces sharp bright maxima where d sinθ = mλ. Because the angle depends on wavelength, it splits white light into colors, with longer wavelengths (red) deflected more than shorter ones (violet).
Detail
Meaning: A grating has many equally spaced slits or ruled lines. Light from every slit spreads by diffraction and the waves interfere, giving bright maxima only where neighboring slits differ in path length by a whole number of wavelengths. More slits make the maxima sharper and brighter than in a double slit. Since the angle depends on wavelength, white light splits into colors, with red deflected more than violet.
Equation: d sinθ = mλ, where d is the slit spacing (m), θ is the angle from the central axis to the maximum (rad), m is the order (0, ±1, ±2, …; unitless), and λ is the wavelength (m).
On the MCAT: Given lines per millimeter and a wavelength, find the first-order angle. Or predict how the pattern changes when λ increases or d decreases (the angles get larger). The highest observable order follows from sinθ ≤ 1. The m = 0 maximum is straight ahead and is not separated by color.
Common confusion: d is the center-to-center spacing, not the width of one slit, and it is the inverse of line density: 500 lines/mm gives d = 2 × 10⁻⁶ m. Finer spacing (smaller d) spreads the pattern wider, not tighter.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.