Question

Interference fringes were produced using light in a double-slit experiment. When a mica sheet of uniform thickness and refractive index $1.6$ (relative to air) is placed in the path of light from one of the slits, the central fringe moves through some distance. This distance is equal to the width of $30$ interference bands if light of wavelength $4800\mathring{A}$ is used. The thickness (in $\mu m$) of mica is

• A. $90$
• B. $12$
• C. $14$
• D. $24$

Answer 1

The correct option is D $24$

Lateral shift $\overline{X}=\frac{\beta }{\lambda }(\mu -1)t=30\beta$

$t=\frac{30\beta \lambda }{\beta (\mu -1)}=\frac{30\times 4800\times {10}^{-10}}{(1.6-1)}=24\times {10}^{-6}=24\mu m$