Diffraction grating: same angle means mλ constant

Steps:

• Diffraction grating equation: d sinθ = mλ, so for fixed θ, mλ is constant.
• For second-order spectrum: m=2, λ=600 nm, so mλ=2×600=1200 nm.
• For third-order spectrum: m=3, λ=? where 3λ=1200 nm.
• Solve: λ=1200/3=400 nm.

Why B is correct:

• 400 nm in third order gives mλ=3×400=1200 nm, matching the grating equation for equal θ.

Why the others are wrong:

• A. 300 nm: 3×300=900 nm, mλ too small.
• C. 600 nm: 3×600=1800 nm, mλ too large.
• D. 900 nm: 3×900=2700 nm, mλ much too large.

Final answer: B