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2. (a) Describe how the ABCD transmission matrix connects the initial and final rays through a biconvex lens with the focal length f. (Explain any notation you use.) [2] a L1 (b) Use the rays illustrated in the diagram to help determine the ABCD transmission matrix from the lens in the paraxial regime. [6] (c) A laser beam is focused to a diffraction limited spot of 1 um diameter. If the total power of the laser is 1kW, what is the pressure at the focal point? [6] (d) It is the intention to produce interference fringes by illuminating a double slit (i.e. Young's experiment) with light at mean wavelength of 500 nm, having a linewidth of 2.5 x 10-3 nm. Calculate the coherence length. At approximately what optical path length difference can you expect the fringes to vanish?

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