Diffraction grating equation determines wavelength from maxima positions

Steps:

• The angle between the two second-order maxima is 10°, so each makes angle θ = 5° with the central maximum.
• Apply the diffraction grating equation: d sin θ = m λ, with d = 1.0 × 10^{-5} m (line spacing), m = 2.
• Rearrange to λ = (d sin θ) / m.
• sin 5° ≈ 0.082, so λ = (1.0 × 10^{-5} × 0.082) / 2 = 4.1 × 10^{-7} m.

Why A is correct:

• It matches λ from d sin θ = m λ using θ = 5°, the standard equation for principal maxima positions in a grating.

Why the others are wrong:

• B assumes m = 1, giving λ = d sin θ ≈ 8.2 × 10^{-7} m.
• C uses sin 5° ≈ 0.088 instead of 0.082.
• D results from approximate sin 10° / 2 without halving the angle correctly.

Final answer: A