A flat piece of glass is supported horizontally above the flat end of a 11.0 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 by light of wavelength 500 nm. As the temperature is slowly increased with 25.0°C, the film changes from bright to dark and back to bright 200 times. What is the coefficient of linear expansion of the metal?