Question

In an interference experiment, when a glass plate of refractive index 1.5 is introduced in the path of one of the beams; fringes are displaced by $x$. When the glass plate is replaced by another transparent plate of same thickness, shift in the fringe is $\frac{3}{2} x .$ Refractive index of $2^{nd}$ transparent plate is

• A. 2.25
• B. 2
• C. 1.75
• D. 1.25

Answer 1

The Correct Option is C

Shift in fringe pattern due to introduction of glass plate in the path. of one of slits in Young's.double slit experiment is given by, $\Delta y = \frac{D(\mu - 1) t}{d}$
Here, $\mu_{1} = 1.5 , \Delta y_{1} =x ,$
$\Delta y_{2} = \frac{3}{2}x, t_{1} = t_{2} = t, \mu_{2} =?$
$\frac{\Delta y_{1}}{\Delta y_{2}} = \frac{\left(\mu_{1} -1 \right)t_{1}}{\left(\mu _{2} -1\right)t_{2}}$
or,$\frac{x}{\frac{3}{2}x} = \frac{\left(1.5 -1\right)}{\left(\mu_{2} -1\right) }$
or, $\mu_{2} -1 = \frac{3}{2} \times0.5$
or, $\mu_{2} = 1+ \frac{3}{4} = \frac{7}{4} = 1.75$