Diffraction grating equation equates path differences for coinciding maxima

Steps:

• Diffraction grating equation: d sinθ = mλ, where d is grating spacing, θ is angle, m is order, λ is wavelength.
• For orange light (λ=600 nm, m=4): d sinθ = 4 × 600 nm = 2400 nm.
• For blue light (m=5): d sinθ = 5 × λ_blue.
• Equate: 5 λ_blue = 2400 nm, so λ_blue = 2400 / 5 = 480 nm.

Why B is correct:

• 480 nm satisfies the grating equation d sinθ = mλ for equal angles in specified orders.

Why the others are wrong:

• A: 450 nm yields 5×450=2250 nm, not matching 2400 nm.
• C: 500 nm yields 5×500=2500 nm, exceeding 2400 nm.
• D: 750 nm yields 5×750=3750 nm, far exceeding 2400 nm.

Final answer: B