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.