Question

A monochromatic light of wavelength $\lambda$ is incident on the slits. The interference pattern is observed on a screen and central maxima is formed at point $O$. Two thin glass plates of thickness $t_1$ and $t_2$ and refractive indices ${\mu }_1$ and ${\mu }_2$ respectively, are placed in front of each of the two slits. It is observed that at point $O$, the central maxima is formed again. Then $\frac{t_1}{t_2}=?$

• A. $\frac{{\mu }_2}{{\mu }_1}$
• B. $\frac{{\mu }_2-1}{{\mu }_1-1}$
• C. $\frac{{\mu }_1-1}{{\mu }_2-1}$
• D. $\frac{{\mu }_1}{{\mu }_2}$

Answer 1

The correct option is B $\frac{{\mu }_2-1}{{\mu }_1-1}$

Change in path difference due to the films is,
$\Delta x=({\mu }_1-1)t_1-({\mu }_2-1)t_2$

As the position of central maxima remains same, the path difference at point $O$ before and after placing the films is same, i.e. zero.

$\Rightarrow ({\mu }_1-1)t_1=({\mu }_2-1)t_2$

$\therefore \frac{t_1}{t_2}=\frac{{\mu }_2-1}{{\mu }_1-1}$

Hence, $\left(B\right)$ is the correct answer.