Q. In Young’s double slit experiment, the fringes are displaced by a distance $x$ when a glass plate of one refractive index 1.5 is introduced in the path of one of the beams. When this plate in replaced by another plate of the same thickness, the shift of fringes is $(3/2)x$. The refractive index of the second plate is
A) 1.75
B) 1.50
C) 1.25
D) 1.00
Explanation
(b) Fringe shift is given by $x = \frac{(\mu - 1)t\beta}{\lambda}$
For first plate, $x = \frac{(\mu_{1} - 1)t\beta}{\lambda}$
For second plate $\frac{3}{2}x = \frac{(\mu_{2} - 1)t\beta}{\lambda}$
$\Rightarrow \left( \frac{\mu_{2} - 1}{\mu_{1} - 1} \right) = \frac{3}{2} \Rightarrow \left( \frac{\mu_{2} - 1}{1.5 - 1} \right) = \frac{3}{2}$
$\Rightarrow \mu_{2} = 1.75$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.