In a standard Young's double-slit experiment with coherent light of wavelength 600 nm, the fringe width of the fringes in the central region (near the central fringe, `P_(0)`) is observed it to be 3 mm. An extremely thin glass plate is introduced to be displaced by 11 mm. Another thin plate is placed before the second slit and it is observed that the fringe are now displaced by an additional 12 mm. If the additional optical path lengths introduced are `Delta_(1)` and `Delta_(2)` then

Options

A. `11 Delta_(1) = 12 Delta_(2)`
B. `12 Delta_(1) = 11 Delta_(2)`
C. `11 Delta_(1) gt 12 Delta_(2)`
D. none of these

Answer

b

Explanation

`S_(1) = (Delta_(1) D)/(d) = 11 xx 10^(-3)`
`S_(2) = (Delta_(2) D)/(d) = 12 xx 10^(-3)`
`implies Delta_(1) // Delta_(2) = 11 // 12`
`rArr 12 Delta_(1) = 11 Delta_(2)`