A Rayleigh interferometer (as shown in the figure below) can be used to measure the index of refraction of air. Two transparent tubes (T₁ and T₂) are placed behind two slits. One of the tubes (T₂) was filled with air already, while the other tube (T₁) was in vacuum at the beginning. Then air was gradually filled into T₁ until reaching the same pressure as T₂.  During this process, it was observed that the intensity at P changed 98.5 times. The tube length was 20 cm, wavelength of light was 589.3 nm. Please calculate the index of refraction of air (to the accuracy of 0.00001).

Hint: the path length of light in a medium equals to the index of refraction times actual length.