Answer: [tex]0.75\ cm[/tex]
Explanation:
Given
Wavelength of light [tex]\lambda=500\ nm[/tex]
Screen is [tex]D=1\ m[/tex] away
Distance between two adjacent bright fringe is [tex]\Delta y=\dfrac{\lambda D}{d}[/tex]
When same experiment done in water, wavelength reduce to [tex]\dfrac{\lambda }{\mu}[/tex]
So, the distance between the two adjacent bright fringe is [tex]\Delta y'=\dfrac{\lambda D}{\mu d}[/tex]
Keeping other factor same, distance becomes
[tex]\Rightarrow \dfrac{1}{\frac{4}{3}}=\dfrac{3}{4}\quad \text{Refractive index of water is }\dfrac{4}{3}\\\\\Rightarrow 0.75\ cm[/tex]
