Question

In Young's double-slit experiment using monochromatic light, the light pattern shifts by a certain distance on the screen when a mica sheet of refractive index $\mu$ and thickness $t$ microns is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the plane of 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 wavelength of light?

• A. $\left(1/2\right)t(\mu -1)$
• B. $t(\mu -1)$
• C. $\mu t$
• D. $3\mu t$

Answer 1

The correct option is A $\left(1/2\right)t(\mu -1)$

Upon introduction of mica sheet, lateral shift $\overline{X}=\frac{\beta }{\lambda }(\mu -1)t$

On removal of mica sheet, new fringe width ${\beta }^{\prime }=\frac{\lambda \left(2D\right)}{d}=2\beta$

but, ${\beta }^{\prime }=\overline{X}\Rightarrow \lambda =\frac{(\mu -1)t}{2}=\left(1/2\right)t(\mu -1)$