A flat piece of glass is supported horizontally above the flat end of a 12.0 cm long metal rod that has its lower end rigidly fixed. The thin film of air among the rod and the glass is observed to be bright when illuminated with light of wavelength 515 nm. As the temperature is slowly increased with 24.0°C, the film changes from bright to dark and back to bright 150 times. What is the coefficient of linear expansion of the metal?