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Q.4 (a) You wish to install a rectangular mirror in your hallway that allows you to see yourself from the top of your head to your toes. i) If the mirror is 1 m wide and vertical and you are 1.7 m tall. what is the minimum height of the mirror from top to bottom? ii) Assuming your eyes are 10 cm from the top of your head, what should the distance between the floor and the bottom edge of this mirror be? (25 marks) (b) As light travels from a vacuum into Pyrex glass does its frequency, wavelength and speed increase, decrease or stay the same? (15 marks) (c) For a Michelson Interferometer describe why it is necessary for the light to be coherent for a sustained interference pattern to be formed. (25 marks) (d) Two hairs are placed between two flat, 10-cm-long glass plates (of refractive index n=1.47 ) with one hair at each end of the plates. When this arrangement is illuminated with light of wavelength λ=500 nm, an interference pattern is observed. The pattern has a total of 20 dark bands. Can you determine any physical characteristic of the hairs? If yes, calculate it. (25 marks) (e) If the same experiment (as in (d)) was performed in a container of glycerol (refractive index =1.47 ) what, if anything, would happen to the interference pattern. Assume that the relative distances of the glass plates and the hairs does not change. (10 marks)