Question

A vessel $\text{ABCD}$ of $\text{10 cm}$ width has two small slits ${\text{S}}_1$ and ${\text{S}}_2$ sealed with identical glass plates of equal thickness. The distance between the slits is $\text{0}\text{.8 mm}$ . $\text{POQ}$ is the line perpendicular to the plane $\text{AB}$ and passing through $\text{O}$ , the



middle point of ${\text{S}}_1$ and ${\text{S}}_2$ , A monochromatic light source is kept at $\text{S}$ , $\text{40 cm}$ cm below $\text{P}$ and $\text{2 m}$ from the vessel, to illuminate the slits as shown in the figure alongside. After a liquid is poured into the vessel and filled upto $\text{OQ,}$ it was found that the central bright fringe is now located at $\text{Q}$ . Calculate the refractive index of that liquid.

• A. $\text{1.0016}$
• B. $\text{2}\text{.0032}$
• C. $\text{1}\text{.0010}$
• D. $\text{1}\text{.0026}$

Answer 1

Answer: (A)

Given, $d=0.8\text{mm}$
${\text{y}}_1=40{\text{ cm, D}}_1=2\text{m}$

Thickness of liquid having refractive index $\mu$ is given by $t=D_2=10\text{cm}$
Initial path difference
${\text{Δx}}_{\text{1}},={\text{ SS}}_1-{\text{SS}}_2=\frac{{\text{y}}_{\text{1}}\text{d}}{{\text{D}}_{\text{1}}}$
For central maxima of $Q$ , optical path difference introduced by liquid of refractive index $\mu$ should be compensate for initial path difference
i.e. $\left(\mu -1\right)t=\Delta x_1$
$\mu =1+\frac{\Delta {\text{x}}_1}{\text{t}}=1+\frac{{\text{y}}_1\text{d}}{{\text{t D}}_1}$
$=1+\frac{0\text{.}4\text{m}\times 0\text{.}8\text{mm}}{0\text{.}1\text{m}\times 2\text{m}}$
$=1+2\times 0\text{.}8\times 10^{-3}$
$=1+1\text{.}6\times 10^{-3}$
$=1\text{.}0016$