Diffraction grating equation equates orders and wavelengths at same angle

Steps:

• Use diffraction grating formula: d sinθ = mλ, where d is spacing, θ is angle, m is order, λ is wavelength.
• For same θ, m_blue λ_blue = m_unknown λ_unknown.
• Substitute values: 3 × 480 nm = 2 × λ_unknown.
• Solve: λ_unknown = (3 × 480) / 2 = 720 nm.

Why B is correct:

• 720 nm satisfies d sinθ = mλ, as 2 × 720 = 1440 equals 3 × 480, matching angles per grating law.

Why the others are wrong:

• A: 320 nm gives 2 × 320 = 640, not equal to 1440, so angles differ.
• C: 480 nm gives 2 × 480 = 960, not equal to 1440, so angles differ.
• D: 1440 nm gives 2 × 1440 = 2880, twice 1440, so angle is larger.

Final answer: B