C} The equation you found in b} describes a set of planes in space. What angle do these planes of constructive interference make with the central axis? d} Thick photographic film is exposed and, once developed, turns dark in the regions where the irradiance is highest, the planes of'constructive interference. This series of parallel planes together acts as a low reflectivity plane mirror parallel to one of the interference planes. For this part of the question, you may simply treat the photographic film as a mirror at the same angle to the central axis as the planes of maximum irradiance. The object is removed, and the same reference wave at E = is now used to \"readout\" the hologram. What angle 3" relative to the central axis will it this \"readout\" wave reflect at? A similar process will occur for every ray that is emitted by the object {i.e., for every angle E that leaves the object]. Explain in two sentences how the set of ray angles from the object is reproduced when, in the absence of the object, the readout wave is sent to the film. In this question, we are going to roughly figure out how a hologram works. Consider a ray coming from an illuminated object. It represents a plane wave at angle 5' to the central axis ofthe system. A \"reference\" plane wave is travelling parallel to the optic axis, with E = I]. All ofthese waves travel in the same sense along the optic axis [i.e., they all travel from left to right, although with different angles 3). Both rays have the same amplitude, frequency, and polarization. W111?\" doing this question, it may be helpful to compare your results to those onuestion 4 on Homework T. The physical situation is very similar, so this previous question can give you an idea of what to expect. Note however that these questions have a different geometry, so your results for this question won't be identical to the other question. a} Express how the phase of the object {(13.3} and reference waves {(1)2} depends on position {i.e., give an expression for the argument of the exponential form ofthe waves in terms of I, z, and E}. b} Show that the waves interfere constructively when Ax + By + CE 2 Inn for integer values ofn, whereA = k Sin B, B = fl, and C = k cos B]. In addition, find a similar condition satisfied by I, y, and a where the waves interfere destructively