Suppose you illuminate two thin slits by monochromatic coherent light in air and find that they produce their first interference minima at \pm 35.09 degrees on either side of the central bright spot. you then immerse these slits in a transparent liquid and illuminate them with the same light. now you find that the first minima occur at \pm 19.48 degrees instead.
a) what is the index of refraction of this liquid?
express your answer using four significant figures.