Diffraction grating equation for maxima

Steps:

• Apply the formula d sinθ = mλ, where d = 2.7 × 10^{-6} m is grating spacing, θ = 53° is the angle, m = 4 is the order.
• Compute sin(53°) = 0.7986 ≈ 0.8.
• Calculate d sinθ = (2.7 × 10^{-6}) × 0.8 = 2.16 × 10^{-6} m.
• Solve for λ = (2.16 × 10^{-6}) / 4 = 5.4 × 10^{-7} m.

Why B is correct:

• 5.4 × 10^{-7} m exactly matches λ from d sinθ = mλ for the given values.

Why the others are wrong:

• A: Too small; results from dividing by 8 instead of 4 (double order error).
• C: Too small; from using cos(53°) ≈ 0.6 instead of sin(53°).
• D: Too small; from using θ = 30° instead of 53°.

Final answer: B