Problem 5.77

Figure 5.16 illustrates an interferometer used in measurements of refractive indices of transparent substances. Here \(S\) is a narrow slit illuminated by monochromatic light with wavelength \(\lambda=589 \mathrm{nm}, 1\) and 2 are identical tubes with air of length \(l=\) \(=10.0 \mathrm{~cm}\) each, \(D\) is a diaphragm with two slits. After the air in tube 1 was replaced with ammonia gas, the interference pattern on the screen \(S c\) was displaced upward by \(N=17\) fringes. The refractive index of air is equal to \(n=1.000277\). Determine the refractive index of ammonia gas.