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.