Question

A two-slit Young's interference experiment is done with monochromatic light of wavelength $6000 \, \overset{^\circ }{A}$ . These slits are $2 \, mm$ apart. The fringes are observed on a screen placed $10 \, cm$ away from the slits. A transparent plate of thickness of $0.5 \, mm$ is placed in front of one of the slits. It is found that the interference pattern shifts by $5 \, mm$ . What is the refractive index of the transparent plate?

• A. $1.2$
• B. $1.5$
• C. $1.8$
• D. $4/3$

Answer 1

Answer: (A)

$\text{Shift} = \left(\mu - 1\right) \frac{\text{tD}}{\text{d}}$
$5 \times 1 0^{- 3} = \left(\mu - 1\right) \times \frac{\left(\text{0.5}\right) \times 1 0^{- 3} \times 1 0 \times 1 0^{- 2}}{2 \times 1 0^{- 3}}$
$⇒ \, \, \, \left(\mu - 1\right) = \frac{1}{5}$
$⇒ \, \, \, \mu = \frac{6}{5} = \text{1.2}$