Students performing a double-slit experiment wish to double the fringe spacing Δy observed on the screen without altering the monochromatic light source already in use. Initially the experiment has slit separation d0=0.20mm and screen distance L0=1.5m. The apparatus allows the students to adjust the slit separation to any value and to reposition the screen freely along a track.
(a) The students consider two independent strategies.
• Strategy I: Halve the slit separation to 21d0 while leaving the screen at L0.
• Strategy II: Double the screen distance to 2L0 while leaving the slit separation at d0.
Using qualitative proportional reasoning, determine which single strategy more effectively achieves the goal of doubling Δy. Explain your choice.
(b) The students ultimately decide to adjust bothd and L. Let the new values be d=αd0 and L=βL0, where α and β are dimensionless factors.
Express the new fringe spacing Δynew in terms of α, β, and the original spacing Δy0 (no numerical substitution required). Then, state a general condition on α and β that must be satisfied to make Δynew=2Δy0. Provide brief reasoning for your expression and condition.