An optics laboratory is designing a demonstration that will display the largest possible double-slit fringe spacing on a projection screen. Practical constraints are as follows:
• Bench length: The distance from the slits to the screen can be set anywhere from 1.0m up to a maximum of 2.5m.
• Adjustable slit assembly: The slit separation d can be chosen in the range 0.050mm≤d≤0.150mm.
• Available lasers: Wavelengths of 405nm (violet), 532nm (green), and 650nm (red) are all on hand.
The demonstration will operate well within the small-angle regime.
(a) Propose specific values of λ, d, and L (each within its allowed range) that together maximize the expected fringe spacing Δy. Clearly state your choices.
(b) Provide a detailed qualitative argument comparing all permitted wavelengths, slit separations, and screen distances to justify why your chosen combination yields the largest Δy under the stated constraints.
(c) Suppose that after the apparatus is built, space limitations force the screen to be moved 0.5 m closer to the slits while all other settings remain unchanged. Estimate the approximate percentage change in Δy produced by this relocation and explain the reasoning steps leading to your estimate.