Question

Young's double slit experiment is made in a liquid. The ${10}^{th}$ bright fringe lies in liquid where $6^{th}$ dark fringe lies in vacuum. The refractive index of the liquid is approximately

• A. $1.8$
• B. $1.5$
• C. $1.3$
• D. $1.6$

Answer 1

Answer: (A)

$1.8$

From the question,

$\left(y_{10}{)}_{bright}\right(liquid)=(y_6{)}_{dark}\left(vacuum\right)$

Equating the fringe positions for bright and dark fringes,

$\frac{n_{bright}\lambda D}{{\mu }_{liquid}d}=\frac{(2\times n_{dark}-1)\lambda D}{2{\mu }_{vacuum}d}$

$\frac{10\lambda D}{{\mu }_{liquid}d}=\frac{(2\times 6-1)\lambda D}{2{\mu }_{vacuum}d}$

$\frac{10}{{\mu }_{liquid}}=\frac{11}{2\left(1\right)}$

${\mu }_{liquid}=\frac{10\times 2}{11}=1.8$

The correct option is A.