Question

In Young's double-slit experiment using monochromatic light of wavelength $\lambda$, the fringe pattern shifts by a certain distance on the screen when a mica sheet of the refractive index $1.6$ and thickness $2.0\mu m$ is introduced in th epath of one of the interfereing 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 the light.

• A. $4500\mathring{A}$
• B. $5700\mathring{A}$
• C. $6000\mathring{A}$
• D. $4000\mathring{A}$

Answer 1

Answer: (C)

$6000\mathring{A}$

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, ${\beta }^{\prime }=\overline{X}\Rightarrow \lambda =\frac{(\mu -1)t}{2}=\frac{(1.6-1)\times 2}{2}=0.6\mu m=6000A^o$