Question

In a Young’s double-slit experiment, a thin sheet of mica is placed over one of the two slits. As a result, the center of the fringe pattern (on the screen) shifts by an amount corresponding to 30 dark bands. The wave length of the light in this experiment is 480 nm and the refractive index of the mica is 1.60. The mica thickness is (approximately) :

• A. $0.090\text{mm}$
• B. $0.012\text{mm}$
• C. $0.014\text{mm}$
• D. $0.024\text{mm}$

Answer 1

The correct option is D $0.024\text{mm}$

30 Dark fringes
$\beta =\frac{\lambda D}{d}$
Shift $=\frac{30\lambda D}{d}$
Shift in central maxima $=\frac{(\mu -1)tD}{d}$
$\frac{(\mu -1)tD}{d}=\frac{30\lambda D}{d}$
$0.60t=30\times 480\times {10}^{-9}$
$t=24\times {10}^{-6}m=24\mu m$
Or $t=0.024\text{mm}$