Answer:
The index of refraction of the gas is [tex]n_g = 1.000922[/tex]
Explanation:
From the question we are told that
The wavelength of light is [tex]\lambda = 560 \ nm = 560 *10^{-9} \ m[/tex]
The length of tube is [tex]L = 5.10 \ cm = \frac{5.10 }{100} =0.0510 \ m[/tex]
The number of fringes is [tex]N = 168[/tex]
Generally the index of refraction of the gas is mathematically repreented as
[tex]n_g = 1 + \frac{N \lambda }{2 L }[/tex]
substituting values
[tex]n_g = 1 + \frac{168 *[ 560* 10^{-9}] }{2 * 0.0510 }[/tex]
[tex]n_g = 1.000922[/tex]
