Diffraction Grating

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.