Question

When a thin transparent sheet of refractive index $\mu =\frac{3}{2}$ is placed near one of the slits in Young's double slits experiment, the intensity at the centre of the screen reduces to half of the maximum intensity. The minimum thickness of the sheet should be ($\lambda$ is the wavelength of light and both slits are identical)

• A. $\frac{\lambda }{4}$
• B. $\frac{\lambda }{8}$
• C. $\frac{\lambda }{2}$
• D. $\frac{\lambda }{3}$
• E. $\frac{\lambda }{5}$

Answer 1

The correct option is C $\frac{\lambda }{2}$

We have intensity,
$I=4I_{o}co{s}^2\left(\frac{\varphi }{2}\right)$
$2I_o=4I_{o}co{s}^2\left(\frac{\varphi }{2}\right)$
$⟹\varphi =\frac{\pi }{2}$
Also, phase difference $x=\frac{2\pi }{\lambda }(\mu -1)t$
$⟹\frac{\pi }{2}=\frac{2\pi }{\lambda }(\frac{3}{2}-1)t$
$⟹t=\frac{\lambda }{2}$