Linear separation in diffraction grating patterns Steps:

• The grating equation is d sinθ = mλ, where d is line spacing, θ is angle, m is order, λ is wavelength.
• For small angles, θ ≈ mλ/d; linear position on screen y ≈ L θ = mλL/d, with L as grating-to-screen distance.
• Separation between consecutive orders Δy ≈ λL/d.
• Increasing L directly increases Δy while keeping the number of spots (seven) the same.

Why A is correct:

• Δy is directly proportional to L per the small-angle approximation y = mλL/d, so larger L spreads the pattern linearly on the screen.

Why the others are wrong:

• B: Increasing frequency f decreases λ (=c/f), reducing Δy.
• C: Intensity changes brightness but not positions or Δy.
• D: Increases lines per meter, decreasing d and thus increasing Δy angularly, but reduces maximum order m_max (=d/λ), potentially eliminating higher spots and compressing the overall pattern.

Final answer: A