Question

In Young's double slit experiment, 5th dark fringe is obtained at a point. If a thin transparent film is placed in the path of one of waves, then 7th bright fringe is obtained at the same point. The thickness of the film in terms of wavelength $\lambda$ and refractive index $\mu$ will be:

• A. $\frac{1.5\lambda }{(\mu -1)}$
• B. $1.5(\mu -1)\lambda$
• C. $2.5(\mu -1)\lambda$
• D. $\frac{2.5\lambda }{(\mu -1)}$

Answer 1

The correct option is D $\frac{2.5\lambda }{(\mu -1)}$

$5^{th}$ dark fringe $=\frac{9}{2}\frac{D\lambda }{d}$
$7^{th}$ bright fringe $=7\frac{D\lambda }{d}$
So, $\frac{9}{2}\frac{D\lambda }{d}+\Delta y=7\frac{D\lambda }{d}$ (By problem)
$\frac{9}{2}\frac{D\lambda }{d}+\frac{D}{d}(\mu -1)t=7\frac{D\lambda }{d}$
$\frac{9}{2}\lambda +(\mu -1)t=7\lambda$
$(\mu -1)t=2.5\lambda$
$t=\frac{2.5\lambda }{\mu -1}$