Compare the times of flight of two light beams one in a tank

Compare the times of flight of two light beams; one in a tank of carbon tetrachloride (n=1.46), the other in air (n=1.0). If the path lengths are made identical, how long must the tank be when a millionth of a second difference in the transit times is required?

Solution

Index of refraction of carbon tetrachloride n=1.46

Index of refraction of air n \' =1.0

Path length L = L

Length in carbon tetrachloride is L \' = nL

Length in air L \" = n \'L

                        = L

So, path difference = L\' - L \"

                            = nL - L

                            = L(n-1)

                            = L (1.46-1)

                            = 0.46 L

Time difference dt = (1/millon) s

                           = (1/10 ⁶) s

                           = 10 ^-6 s

We know dt = path difference / c

             10^-6 = 0.46 L /(3 x10 ⁸ )

                 L = 10 ^-6 x 3 x10 ⁸ /(0.46)

                    = 652 m