A monochromatic light source iluminates a double slit and the interference pattern is seen on a distant screen

Question

Let d = centre-to-centre slit spacint, a = individual slit width, D = screen-to-slit distance, and l = adjacent dark line spacing in the interference pattern.

a) Find the wavelength of light in terms of these parameters

b)How would the dark line spacing change if the whole experiment was immersed in water of refractive index n

Answer 1

angular spacing theta = arctan(I/D)

Wavelength lambda (exact) = d*sin(theta)

lambda (sm. ang. approx.) = d*I/D

If the apparatus were immersed in a medium of R.I. = n, the wavelength would be reduced by 1/n. The same equations would apply, so the line spacing would be smaller.

Hyperphizz (ref.) explains it well.