Question

A mica sheet of thickness $1.964\mu m$ and refractive index $1.6$ is placed in the path of one of the interfering waves. Now the mica sheet is removed and the distance between the slit and the screen is doubled. If this states the distance between two consecutive maxima or minima is equal to the displacement of fringe pattern on placing mica sheet, the wavelength of monochromatic light used is

• A. $5892A^o$
• B. $5269A^o$
• C. $6271A^o$
• D. $3875A^o$

Answer 1

The correct option is A $5892A^o$

Path difference introduced due to insertion of mica sheet $=t(\mu -1)$

Distance between two consecutive maxima $=\frac{2D\lambda }{d}$

Path difference between these points $=\frac{yd}{D}=\frac{\left(\frac{2D\lambda }{d}\right)d}{D}=2\lambda$
hence $t(\mu -1)=2\lambda$

hence $\lambda =5892A^{\circ }$