Question

When a thin transparent plate of refractive index 1.5 is introduced in the path of one of the interfering beams, 20 fringes shift. If the plate is replaced by another plate of refractive index 1.6 and half the thickness, the number of fringes that are displaced is

• A. 20
• B. 12
• C. 6
• D. 18

Answer 1

Answer: (B)

12

Answer 2

Number of fringes shifted,
$N= \frac{shift}{fringe width} =\frac{\left(\mu -1\right)t}{\lambda}$
or, $N \propto\left(\mu -1\right)t$ (for same $\lambda$)
$\therefore \, \frac{N_{1}}{N_{2}} = \frac{\left(\mu_{1} - 1 \right)t_{1}}{\left(\mu_{2} - 1\right)t_{2}}$
Here, $\mu_{1} = 1.5 , t_{1} =t, N_{1} =20 \mu_{2} =1.6, t_{2} = t 2 , N_{2} =?$
or, $\frac{20}{N_{2} } = \frac{\left(1.5 -1\right)t}{\left(1.6 -1\right)\left(t 2\right)} = \frac{2 \times0.5 }{0.6}$
or, $N_{2} =12$