Question

In a $\text{YDSE}$ setup shown in diagram a thin mica sheet $(\mu =1.5)$ is placed in front one of the slits. If the central maxima shifts by $0.4\text{cm}$, then what is the thickness of the mica sheet?

• A. $2\mu \text{m}$
• B. $20\mu \text{m}$
• C. $10\mu \text{m}$
• D. $8\mu \text{m}$

Answer 1

The correct option is D $8\mu \text{m}$

The expression for shift in the central maxima when a sheet is introduced in one of the slits is given by

$\Delta y=\frac{D}{d}(\mu -1)t$

$D$ - Distance between slits and the screen
$d$ - Distance between the two slits
$\mu$ - Refractive index of the sheet
$t$ - Thickness of the sheet

Substituting the data given in the question,

$0.4\times {10}^{-2}=\frac{1}{0.1\times {10}^{-2}}(1.5-1)t$

$\Rightarrow t=8\times {10}^{-6}\text{m}=8\mu \text{m}$

Hence, option $\left(d\right)$ is correct.