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4. Pairs of quarter-wavelength thin-films formed by zirconium oxide (n=2.1) and magnesium fluoride (n=1.38) are used to make a mirror reflecting back into air (n=1)

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4. Pairs of quarter-wavelength thin-films formed by zirconium oxide (n=2.1) and magnesium fluoride (n=1.38) are used to make a mirror reflecting back into air (n=1) with >99.94% reflectivity at 1550nm wavelength on a sapphire substrate (n=1.76). What is the minimum number of pairs of thin films needed to achieve the desired reflectivity? [10 marks ](0=8.8541012F/m;0=1.2566106H/m)

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