Ei 55 d=4a -film Je Consider the interference pattern from a double-slit arrangement as shown. Take d=4a. The wavelength of the monochromatic light incident upon the slits is = 2a/3 (in air). The light emerging from the lower slit passes throgh a transparent film of thickness a/2 and index of refraction n=1.60 (you can take Nair as 1.00). This film also reduces the amplitude of the electromagnetic wave passing through it to 1/3 of its initial value. (a) What is the change in phase introduced by the film for the wave passing through it? (b) What is the expression for the phase difference between the waves from the two slots, as a function of e? (c) Where is the central maximum of the interference pattern, i.e., what is the value of be where m=0? (Hint: Use the result above.) (d) Draw a phasor diagram for the electric field phasors of slits 1, 2, and the total field. (e) Derive an expression for the intensity I as a function of O and other relevant parameters. Express your answer in terms of I., the intensity at the center of the screen where 0=0. (Note that the center of the diffraction pattern is still at 6=0.)