In a Young's double slit experiment using monochromatic light, the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 microns is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the slits and screen is doubled. It is found that the distance between successive maxima now is the same as observed fringe shift upon the introduced of the mica sheet . Calculate the wavelength of the monochromatic light used in the experiment .

Options

A. `(1 // 2)t (mu - 1)`
B. `t (mu - 1)`
C. `mu t`
D. `3 mu t`

Answer

a

Explanation

When mica sheet of thickness t and refractive index `mu` is introduced in the path of one of the interferring beams, optical path increase by `(mu - 1)t`. Therefore, the shift on the screen is given by
`y_(0) = (D)/(d) (mu - 1) t`
When the distance between the plane of slits and screen is changed form D to 2D, then
`beta = (2D)/(d) lambda`
`:. (D)/(d) (mu - 1) t = (2D (lambda))/(d) implies lambda = (1)/(2) (mu - 1)t`