Question

In Young's Double slit experiment, a thin glass mica strip of thickness $(t=8\lambda )$ is pasted infront of slit $S_1$. The same strip is now shifted in front of other slit $S_2$. If the number of fringes which will cross the central point on the screen is N. Find N ? $(d>>D,\lambda <<dand{n}_{mica}=1.5)$

Answer 1

When the mica sheet is placed anywhere in the path of the beam, the net path difference is given by,
$(\mu -1)t=n\lambda$
where $\mu$ is the refractive index of mica, $t$is the thickness, $n$ is the number of shifted fringes and $\lambda$ is the wavelength.
Given $\mu =1.5$, $t=8\lambda$
$⟹(1.5-1)8\lambda =n\lambda$
$⟹n=4$
If the number of fringes which will cross the central point on the screen is $N$, then
$N=2n=8$
Hence the total number of fringes shifted is $8$.