In a Michelson interferometer some light travels from a source to beam splitter. Half the light is sent along arm 1, a distance d1 to mirror 1 where it is reflected. The other half travels a distance d2 to mirror 2. The light is recombined and the interference pattern observed. Mirror 1 Source Beam splitter 6 Interferometer Figure 'l. A Michelson interferometer is set up which splits light up into two paths and recombines them at a detector to observe interference. Part 1) Write an expression for the path difference between the light traveling along the two arms. (Neglect the path difference due to passage through the beam splitter.) Write an expression for the path difference between the light traveling along the two arms. (Neglect the path difference due to passage through the beam splitter.) Part 2) Light with a wavelength of 609 nm is sent along the arms. An interference maximum is observed. Then length of arm 2 is increased (arm 1 is not changed) until a minimum is observed. What was the change in length of arm 2? Part 3) Once again the arms are set to a length that gives an interference maximum. Now a material with length l and refractive index n = 1.53 is inserted into arm 1 as shown in the diagram. What is the minimum length the material can have and give a minimum in the interference pattern? The light (of the same wavelength as in part 2) passes through the material, it is not reflected off it. Mirror 1 d1 Mirror 2 Interferometer Figure 2. A block of length / and refractive index n is placed between the beam splitter and mirror 1. min nm