A double slit apparatus is fitted with a mica strip and a...

The fringe-width in a Young's double slit experiment is independent of the transparent strips placed in front of the slits. The strips only introduce a constant path difference which causes a shift in the entire interference pattern, but the distance between consecutive fringes remains unchanged.

The formula for fringe-width is given by:

$\beta = \dfrac{\lambda D}{d}$

Given values are:
Wavelength of light, $\lambda = 590 \text{ nm} = 590 \times 10^{-9} \text{ m}$
Distance of the screen, $D = 1 \text{ m}$
Separation between the slits, $d = 0.12 \text{ cm} = 1.2 \times 10^{-3} \text{ m}$

Substituting these values into the formula:

$\beta = \dfrac{590 \times 10^{-9} \times 1}{1.2 \times 10^{-3}}$

$\beta = 491.67 \times 10^{-6} \text{ m}$

$\beta \approx 4.9 \times 10^{-4} \text{ m}$