The following figure shows a Rayleigh refractometer. Light from coherently illuminated slits goes through separate hollow airtight arms of length L each with glass entry and exit windows. The separate beams are brought together by a lens with fringes appearing in the image plane. Both arms are initially evacuated, and gas is introduced slowly into one arm. This causes the fringes to move across the field of the view, up or down in the diagram. If m fringes pass through the center of the field while the gas is entering, show that the refractive index of the gas, n, is given by n1=mi/L Source Slits Gas filled tube and A ' A pinhole rf""\"' Evacuated tube Fringes