Question

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 R.I. 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 the screen is doubled. It is found that the distance between successive maxima (or minima) now is the same as the observed fringe shift upon the introduction of the mica sheet. Calculate the wave length of the monochromatic light used in the experiment.

• A. 1180 nm
• B. 590 nm
• C. 689 nm
• D. 500nm

Answer 1

Answer: (B)

590 nm

Answer 2

$\frac{(\mu - 1)tD}{d} = \frac{(2D)\lambda}{d}$

$\mathbf{\lambda =}\frac{\mathbf{(\mu}\mathbf{-}\mathbf{1)t}}{\mathbf{2}}\mathbf{=}\frac{\mathbf{(1.6}\mathbf{-}\mathbf{1)(1.964}\mathbf{\times}\mathbf{1}\mathbf{0}^{\mathbf{-}\mathbf{6}}\mathbf{)}}{\mathbf{2}}$

= 0.589 × 10^–6m

590nm