Separated by a distance of 1.0 cm , two narrow slits emit light in...

Given:
Distance between slits, $d = 1.0 \text{ cm} = 1.0 \times 10^{-2} \text{ m}$
Wavelength, $\lambda = 5.0 \times 10^{-7} \text{ m}$
Distance to screen, $D = 1.0 \text{ m}$

The separation between consecutive maxima is the fringe width, given by:
$\beta = \dfrac{\lambda D}{d}$

Substituting the given values:
$\beta = \dfrac{5.0 \times 10^{-7} \times 1.0}{1.0 \times 10^{-2}} = 5.0 \times 10^{-5} \text{ m}$

$\beta = 0.05 \times 10^{-3} \text{ m} = 0.05 \text{ mm}$

The resolution limit of the human eye is approximately $0.1 \text{ mm}$. Since the fringe width $0.05 \text{ mm}$ is less than the resolution limit of the human eye, the consecutive maxima cannot be distinguished with the naked eye.