or the parts the below question, fill in the empty boxes with your answer (YOUR ANSWER MUST BE ONLY A NUMBER; DO NOT WRITE UNITS; DO NOT WRITE LETTERS). Consider a glass tube with has a length of \( 1051 \mu \mathrm{m} \). The tube is filled with a gas \( (n=1.05) \) and positioned in front of one of the secondary sources in Young’s double slit experiment. The sources are illuminated by a laser beam of vacuum wavelength \( \lambda_{0}=710 \mathrm{~nm} \). a) [1 point] Which formula can be used to calculate the optical path length of a wave (refer to the formula sheet and select the number of the correct formula from the list)? b) [10 points] Calculate the optical path length of the wave passing through the tube, in SI units. \( O P L= \) c) [10 points] The gas is now removed from the tube and the tube is completely filled with a transparent material (of index \( n_{m} \) ). On comparing the fringe pattern corresponding to the gas with that of the material, it is found that the entire interference pattern on the viewing screen is displaced by 323 bright bands toward the side containing the tube. Determine the index of refraction of the material \( n_{m} \).

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