A steady interference pattern is observed in a Young's double slit chamber originally filled with ai

Question

A steady interference pattern is observed in a Young's double slit chamber originally filled with air. If the chamber is suddenly filled completely with a dense transparent gas of refractive index $\mu > 1$, what will physically happen to the total number of interference fringes visible within a fixed central region of the screen?

Professor PC Thomas Classes · Answer

(a) : When the chamber is filled with a medium of refractive index $\mu$, the wavelength of light decreases ($\lambda' = \lambda/\mu$). As a result, the physical fringe width $\beta$ also decreases proportionally ($\beta' = \beta/\mu$). Because the fringes become narrower and are spaced closer together, more individual fringes will be packed into the same fixed observing region on the screen, meaning the total number of visible fringes increases.