A Young's double-slit experiment has a usable screen extending from y = −4β to y = +4β. Initially, all bright fringes lying in this interval are visible. A transparent slab is inserted in front of one slit and shifts the entire interference pattern by +2.5β without changing the fringe width. How many of the bright fringes that were initially visible move outside the usable screen?
Physics · Wave Optics · young's dubble slit experiments
JEE Mains NEET JEE Advanced

Question

A Young's double-slit experiment has a usable screen extending from y = −4β to y = +4β. Initially, all bright fringes lying in this interval are visible. A transparent slab is inserted in front of one slit and shifts the entire interference pattern by +2.5β without changing the fringe width. How many of the bright fringes that were initially visible move outside the usable screen?

Physics · Wave Optics · young's dubble slit experiments

G1 Physics · Accepted Answer

Initially, bright fringes are at y = mβ. Within −4β ≤ y ≤ +4β, the initially visible bright orders are m = −4, −3, −2, −1, 0, 1, 2, 3, 4. After the slab is inserted, every bright fringe shifts by +2.5β. Thus an initially visible order m moves to y' = (m+2.5)β. Check the positive-edge condition: m+2.5 > 4 gives m > 1.5. Therefore the initially visible fringes with m = 2, 3, 4 move beyond the positive edge of the usable screen. No initially visible fringe escapes through the negative edge because…