Question

A thin mica sheet of thickness $2 \times 10^{-6} m$ and refractive index $(\mu=1.5)$ is introduced in the path of the first wave. The wavelength of the wave used is $5000 \, \mathring{A}$ The central bright maximum will shift:

• A. $2$ fringes upward
• B. $2$ fringes downward
• C. $10$ fringes upward
• D. None of these

Answer 1

Answer: (A)

Shift $=\frac{\beta}{\lambda}(\mu-1) t$
$=\frac{\beta(1.5-1) 2 \times 10^{-6}}{5000 \times 10^{-10}}$
shift $=\frac{\beta \times 0.5 \times 2 \times 10^{-6}}{5000 \times 10^{-10}}$
shift $=\frac{\beta \times 0.5 \times 2 \times 10^{-6}}{5 \times 10^{-7}}$
shift $=2 \beta$ i.e., 2 fringes upward