Question

Young's double slit experment is first performed in air and then in a medium other than air. It is found that $8th$ bright fringe in the medium lies where $5th$ dark fringe lies in air. The refractive index of the medium is nearly :

• A. 1.59
• B. 1.69
• C. 1.78
• D. 1.25

Answer 1

The Correct Option is C

$(y_8) $ Bright, medium = $(y_5)$ Dark, air
$\frac{8 \lambda_m D}{d} = \left( \frac{2 (5) - 1}{2} \right) \frac{\lambda D}{d}$
$ \frac{8 \lambda}{\mu} \frac{D}{d} = \frac{9}{2} \frac{\lambda D}{d}$
$\Rightarrow \mu = \frac{16}{9} = 1.78$