Diffraction Grating
N slits — sharper, brighter principal maxima at d sinθ = mλ.
Key Notes
A diffraction grating is a large number N of equally-spaced parallel slits of width a and spacing d.
Principal maxima at d sin θ = mλ — same condition as YDSE bright fringes — but sharpened by the multi-slit interference.
Peak intensity of a principal max scales as N²·I₀, but the angular width shrinks as 1/N — so total power scales as N (energy is conserved).
Between two principal maxima there are (N − 2) secondary maxima — all very faint compared to principal.
Resolving power R = λ/Δλ = m·N. Larger N or higher order m → finer wavelength discrimination.
Single-slit diffraction envelope (sin α/α)² modulates the entire grating pattern. Missing orders when this envelope hits a zero.
Used in spectrometers to disperse light by wavelength — different m's spread different λ's at different angles.
Formulas
Principal maxima
Same as YDSE bright fringes; here it gives the sharp peaks.
Intensity
Combined multi-slit interference × single-slit diffraction.
Resolving power
Smallest wavelength difference the grating can separate at order m.
Angular width of principal max
Decreases linearly with N — peaks become very sharp for fine gratings.
Missing orders
Principal max at order m vanishes if it coincides with a single-slit minimum at m'.
Important Points
A grating with 10,000 lines/cm has d = 1 μm. For visible light, only orders m = 0, ±1, ±2 typically exist (since sin θ ≤ 1).
Higher orders are dispersed more (Δθ ∝ m for small angles) but are weaker because of the single-slit envelope.
Reflection gratings (e.g., CD/DVD surfaces) work on the same principle — used to make rainbow patterns.
Wavelength measurement via grating: λ = (d sin θ)/m at a measured angle. Spectrometers convert this to spectra.
If grating is illuminated with white light, m = 0 stays white, but m ≥ 1 shows the entire visible spectrum spread out — different from a prism (which depends on n(λ)).
Diffraction Grating notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.