Explain how a grating of known line density can measure laser wavelength without a spectrometer. Specify normal incidence, the zero-order reference, order identification, measured distances, processing, uncertainty and safety. A 500 lines mm⁻¹ grating produces first-order spots with y=0.400 m and D=1.20 m. Calculate λ without a small-angle approximation.

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Use d=1/(500×10³)=2.00×10⁻⁶ m; θ measured from undeviated beam, sinθ=0.400/√(1.20²+0.400²)=0.316228, λ=6.32×10⁻⁷ m. Repeat and average sides, check alignment and terminate beams safely. Identify laser, known grating, screen, holders and length measurements. Set grating normal along beam and screen perpendicular to the central beam. Identify n=0 and count nth-order spots; measure D and y from n0. Use d=1/N and sinθ=y/√(D²+y²), then λ=d sinθ/n. Obtain 632 nm. Repeat/average sides and evaluate finite spot/length uncertainty and alignment. State laser precautions.

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