In the ideal double-slit experiment, when a glass-plate(refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wave-length `lamda`), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

Options

A. `2lamda//3`
B. `lamda`
C. `lamda//3`
D. `2lamda`

Answer

D

Explanation

Due to the interoduction of the plate of thickness 't', the fringe pattern is shifted through
`Delta y=(mu-1)t` . . . (1)
For the central maximum to be replaced by its neghbouring maximum, the path difference must change by `lamda`. [This is for the minimum thickness. Otherwise `lamda` can change by `2lamda,3lamda`, . . ]
`therefore Delta y=lamda`
`therefore ` From (1) and (2), `(mu-1)t=lamda`
`therefore t=(lamda)/((mu-1))=(lamda)/((3)/(2)-1)=2lamda`