Understanding Refractive Index Measurement in Interference Patterns

[Joza]

How can one measure refractive index by knowing the change in angular range of the first dark bands of an interference pattern(single slit diffraction), when the apparatus is change from air to under water?

I think I missed that lecture, and I am still catching up.

 

[quantumdude]

You need to know that it's the wavelength, not the frequency, that changes when the refractive index changes. If light has wavelength $\lambda$ in vacuum, then it has wavelength $\lambda^{\prime}=\lambda/n$ in a medium of refractive index $n$.