In the shown YDSE, a point source is 50 cm from the slit plane and 0.5 cm below the central axis; the screen is 1 m beyond the slits. If the source moves toward the screen at 1 mm/s, the instantaneous speed of the central maximum is α×10⁻ᵝ m/s upward. Find α+β.

Question

G1 Physics · Accepted Answer

For source transverse offset yₛ and source distance a, the central maximum is at y=Dyₛ/a. With yₛ=0.005 m, a=0.50 m and D=1 m, and source speed 0.001 m s⁻¹ toward the slit plane, dy/dt=Dyₛv/a²=2×10⁻⁵ m s⁻¹. Thus α=2, β=5 and α+β=7.